## Albert-Ludwigs-Universität Freiburg## Mathematisches Institut## Prof. Guofang Wang |

- Seit 1.10.2009 W3 Professor, Freiburg Uni.
- 1.10.2006--30.9.2009, W2 Professor, Magdeburg Uni.
- 1.9.1999--30.9.2006, Mitarbeiter, Max-Planck-Inst. Math., Leipzig
- 1.10.1998--30.09.1998, Asso Prof., Academica Sinica, Beijing
- 1.9.1996--31.12.1997, Gastwissenschaftler, Max-Planck-Inst. Math., Leipzig
- 1.10.1994--30.08.1996, Gastwissenschaftler, Ruhr-Uni. Bochum.
- 1.9.1990--30.09.1994, Ass. Prof., Asso Prof., Academica Sinica, Beijing
- 1.9.1980--30.0.1990, Bechelor, Zhejiang Uni. (1984), Master, Hangzhou Uni. (1987), Ph.D, Academica Sinica, Beijing (1990)

- Associate Editor for Annals Global Analysis and Differential Geometry (since 01/2012)
- Associate Editor for Advances in Calculus of Variations (since 01/2018)
- Associate Editor for Journal of Mathematical Study (since 01/2019)
- Associate Editor for SN Partial Differential Equations and Applications (since 01/2020)

**The Dirichlet problem for the equation of prescribed mean curvature**, Ann. Inst. Henri Poincare, Analyse non lineaire, 9 (1992), 643--655.**Non-symmetric harmonic maps from annuli to 2-sphere,***C.R. Acad. Sci., Paris, 315 (1992), 699--702.***Harmonic maps from a closed surface of higher genus to the unit 2-sphere***International J. of Math.*4 (1993) 359--365.**(with W.Y.Ding)N onexistence of smooth axially symmetric harmonic maps from $B^3$ into $S^2$,***Nonlinear P.D.E., Proceeding of International Conference, ed. G. Dong und F.H. Lin*(1993) 38--45. J. Part. Diff. Eq., 24 (2011), pp. 289-296.**(with J. Jost, X. Peng) Analytical aspects of the Seiberg-Witten functional,***Calc. Var. and P.D.E.*4 (1996) 205-218.**Birkhoff minimax principle for minimal surfaces with free boundary,***Math. Ann.*314 (1999) 1, 89-107**(with Ding, W., Jost, J., Li, J.)The differential equation $\Delta u = 8\pi - 8\pi he^u$ on a compact Riemann surface,***Asian J. Math.*1 (1997) 230-248**(with W. Ding, J. Jost, J. Li) An analysis of the two-vortex case in the Chern-Simons Higgs model***Calc. Var. and P.D.E.*7 (1998) 87-97**(with X. Peng) Harmonic maps with a prescribed potential,***C. R. Acad. Sci. Paris*327 (1998) 271-276**(with Ding, W., Jost, J., Li, J.) Multiplicity results for the two-vortex Chern-Simons Higgs model on the two-sphere,***Commemt. Math. Helv.*74 (1999) 118-142**(with L. Zhang) Non-Topological Solutions of the Relativistic SU(3) Chern-Simons Higgs Model***Comm. Math. Phys.*202 (1999) 3, 501-515**Moser-Trudinger inequalities and Liouville systems***C. R. Acad. Sci. Paris*328 (1999), 895-900**(with W. Ding, J. Jost, J. Li) Existence results for mean field equations,***Ann. Inst. Henri Poincar\' e, Analyse non lin\'eaire*16 (1999), 653-666**S^1-invariant harmonic maps from S^3 to S^2***Bull. London Math. Soc.*32 (2000), 729--736**(with J. Wei) On a conjecture of Wolansky,***Nonlinear Analysis, TMA.*48 (2002) 927-1075**(with X. Zhu) Extremal Hermitian metrics on Riemann surfaces with singularities***Duke J. Math.*104 (2000), 181--210**(with H. V. Le)A characterization of minimal Legendrian submanifolds in {S}^{2n+1}***Composito Math.*129 (2001), 87-93**(with H. V. Le) Anti-complexified Ricci flows on symplectic manifolds***J. reine angew. Math.,*530 (2001) 17-32**(with W. Ding, J. Jost, J. Li, X. Peng)Self duality equations for Ginzburg-Landau and Seiberg-Witten type functionals with $6^{th}$ order potentials,***Commun. Math. Phys.*217 (2001) 2, 383-407**(with J. Wei)Steady state solutions of a reaction-diffusion system modeling chemotaxis,***Math. Narich.*233-234 (2002) 221-236**Nirenberg's problem on domains,***J. Geom. Anal.,*11 (2001), 717-726**(with D. Horstmann) Blowup in a chemotaxis model without symmetry assumptions,***Europ. J. of Appl. Math.*12 (2001), 159-177**(with J. Jost) Analytic aspects of the Toda system: I. Moser-Trudinger inequalities,***Comm. Pure Appl. Math.,*54 (2001), 1289-1319**(with J. Jost) Classification of solutions of a Toda system in R^2,***International Math. Research Notices,*2002 (2002) 277-290**(with P. Guan) A fully nonlinear conformal flow on locally conformally flat manifolds,***J. reine angew. Math.*557 (2003) 219-238**(with P. Guan) Local estimates for a class of fully nonlinear equations arising from conformal geometry,***International Math. Research Notices,*2003 (2003) 1413-1432**(with Dong Ye) On a nonlinear elliptic equation arising in a free boundary problem,***Math. Z.,*244 (2003) 531-548**(with P. Gaun and J. Viaclovsky)Some p roperties of the Schouten tensor and applications to conformal geometry,***Trans. AMS,*355 (2003), 925-933**(with P. Guan and C.-S. Lin) Application of The Method of Moving Planes to Conformally Invariant Equations,***Math Z.,*247 (2004) 1-19**(with P. Guan) Geometric inequalities on locally conformally flat manifolds,***Duke J. Math.*124 (2004), 177-212**(with C. Chen and C.-S. Lin) Existence of bubbling phenomena of two-vortex solutions in a Chern-Simons Model***Annali della Scuola Normale Superiore, Classe di Scienze,*Serie V, 3 (2004), 367-397**(with Fei, S.-M. Jost, J. Li-Jost, X.) Entanglement of formation for a class of quantum states,***Phys. Lett. A*310 (2003), 333--338.**(with J. Jost, C. S. Lin) Analytic Aspects of the Toda System: II. Bubbling Behaviors of Solutions,***Comm. Pure Appl. Math*59 (2006), no. 4, 526--558.**(with P. Guan and C.-S. Lin) Schouten tensor and some topological properties,***Comm. Anal. and Geom.*13 (2005), no. 5, 887--902**(with Knut Smoczyk, Yuan-Long Xin) Bernstein type theorems with flat normal bundle***Calc. Vari.,*26 (2006), no. 1, 57--67.**(with Q. Chen, J. Jost, J. Li) A Regularity Theorem and Energy Identities for Dirac-Harmonic Maps,***Math. Z.*251 (2005), no. 1, 61--84.**(with Q. Chen, J. Jost, J. Li) On Dirac-harmonic maps***Math. Z*254 (2006), no. 2, 409--432.**$\sigma_k$σk-scalar curvature and eigenvalues of the Dirac operator.***Ann. Global Anal. Geom.*30 (2006), no. 1, 65--71.**(with Yuxin Ge) On a fully nonlinear Yamabe problem.***Ann. Sci. École Norm. Sup.*(4) 39 (2006), no. 4, 569--598.**(with P. Guan) Conformal deformations of the smallest eigenvalue of the Ricci tensor.***Amer. J. Math.*129 (2007), no. 2, 499--526.**(with Guan, Pengfei ; Lin, Chang-Shou) Local gradient estimates for quotient equations in conformal geometry**Internat. J. Math. 18 (2007), no. 4, 349--361.- (with Ge, Yuxin)
**On a conformal quotient equation.**Int. Math. Res. Not. IMRN*2007, no. 6, Art. ID rnm019, 32 pp.* - (with Jost, Jürgen; Zhou, Chunqin)
**Super-Liouville equations on closed Riemann surfaces.**Comm. Partial Differential Equations 32 (2007), no. 7-9, 1103--1128. - Chen, Q. ; Jost, J. ; Wang, G. Liouville theorems for Dirac-harmonic maps. J. Math. Phys. 48 (2007), no. 11, 113517, 13 pp.
- (with Jost, Jürgen ; Ye, Dong ; Zhou, Chunqin) The blow up analysis of solutions of the elliptic sinh-Gordon equation. Calc. Var. Partial Differential Equations 31 (2008), no. 2, 263--276.
- (with Chen, Qun ; Jost, Jürgen) Nonlinear Dirac equations on Riemann surfaces. Ann. Global Anal. Geom. 33 (2008), no. 3, 253--270.
- (with Jost, Jürgen ; Zhou, Chunqin) Metrics of constant curvature on a Riemann surface with two corners on the boundary. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 2, 437--456.
- (with Jost, Jürgen; Zhou, Chunqin) Metrics of constant curvature on a Riemann surface with two corners on the boundary. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 2, 437–456,
- (with Jost, Jürgen; Wang, Zhou, Chunqin; Zhu, Miaomiao) Energy identities and blow-up analysis for solutions of the super Liouville equation. J. Math. Pures Appl. (9) 92 (2009), no. 3, 295–312.
- (with Shi, Yuguang; Wu, Jie) On the behavior of quasi-local mass at the infinity along nearly round surfaces. Ann. Global Anal. Geom. 36 (2009), no. 4, 419–441.
- (with Futaki, Akito; Ono, Hajime) Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds. J. Differential Geom. 83 (2009), no. 3, 585–635.
- (with Chen, Wenxiong; Li, Congming) On the stationary solutions of the 2D Doi-Onsager model. Nonlinear Anal. 73 (2010), no. 8, 2410–2425
- (with Smoczyk, Knut ; Zhang, Yongbing) The Sasaki-Ricci flow. Internat. J. Math. 21 (2010), no. 7, 951–969.
- (with Ge, Yuxin ; Lin, Chang-Shou) On the σ2-scalar curvature. J. Differential Geom. 84 (2010), no. 1, 45–86.
- (with Chao Xia) A Brunn-Minkowski inequality for a Finsler-Laplacian. Analysis (Munich) 31 (2011), no. 2, 103–115.
- (with Xia, Chao) A characterization of the Wulff shape by an overdetermined anisotropic PDE. Arch. Ration. Mech. Anal. 199 (2011), no. 1, 99–115.
- (with Yuxin Ge) An almost Schur theorem on 4-dimensional manifolds. Proc. Amer. Math. Soc. 140 (2012) 1041-1044.
- (with Chao Xia) Blow-up analysis of a Finsler–Liouville equation in two dimensions Journal of Differential Equations, 252 (2012) no. 2, 1668-1700
- (with Dong Ye) A Hardy–Moser–Trudinger inequality Advances in Mathematics, 230 (2012) no. 1, 294-320
- (with Jin, Y.; Jost, J.) A nonlocal version of the Osher-Solé-Vese model. J. Math. Imaging Vision 44 (2012), no. 2, 99–113.
- (with Xu, Deliang) Harmonic maps from smooth metric measure spaces. Internat. J. Math. 23 (2012), no. 9, 1250095,
- (with Xia, Chao) An optimal anisotropic Poincaré inequality for convex domains. Pacific J. Math. 258 (2012), no. 2, 305–325.
- (with Zhang, Yongbing) A conformal integral invariant on Riemannian foliations. Proc. Amer. Math. Soc. 141 (2013), no. 4, 1405–1414.
- (with Chen, Q.; Jost, J.) The maximum principle and the Dirichlet problem for Dirac-harmonic maps. Calc. Var. Partial Differential Equations 47 (2013), no. 1-2, 87–116.
- (with Q. Chen, J. Jost and Miaomiao Zhu) The boundary value problem for Dirac-harmonic maps, J. Eur. Math. Soc. (JEMS). Volume 15, Issue 3, 2013, pp. 997-1031.
- (with Yongbing Zhang) The Sasaki-Ricci flow on Sasakian 3-spheres, Communications in Mathematics and Statistics: Volume 1, Issue 1 (2013), Page 43-71
- (with Y. Ge) On a conformal quotient equation. I, Comm. Anal Geom. 21 (2013), no. 1, 1–38.
- (with Y. Ge, Chao Xia) On problems related to an inequality of Andrews, De Lellis and Topping, IMRN, Int Math Res Notices (2013) Vol. 2013 4798-4818 doi:10.1093/imrn/rns196
- (with Ge, Yuxin)A new conformal invariant on 3-dimensional manifolds. Adv. Math. 249 (2013), 131–160.
- (with Chao Xia) A sharp lower bound for the first eigenvalue on Finsler manifolds, Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), no. 6, 983–996.
- (with Xia, Chao) Isoperimetric type problems and Alexandrov-Fenchel type inequalities in the hyperbolic space, Adv. Math. 259 (2014), 532–556.
- (with Y. Jin, J. Jost) A New Nonlocal H 1 Model for Image Denoising, to appear in Journal of Mathematical Imaging and Vision, no. 1, 93–105.
- (with Y. Ge and J. Wu) The GBC mass for asymptotically hyperbolic manifolds The GBC mass for asymptotically hyperbolic manifolds, (Announcement) C. R. Math. Acad. Sci. Paris 352 (2014), no. 2, 147–151.
- (with J. Jost, C. Zhou M. Zhu) The boundary value problem for the super-Liouville equation, to appear in Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 4, 685–706
- (with Yuxin Ge, Jie Wu) The Gauss-Bonnet-Chern mass of conformally flat manifolds, arXiv:1212.3213, Int Math Res Notices (2014) 2014 (17): 4855-4878. doi: 10.1093/imrn/rnt095
- (with Yuxin Ge, Jie Wu) Hyperbolic Alexandrov-Fenchel quermassintegral inequalities II, arXiv:1304.1417, J. Diff. Geom. 98 (2014), no. 2, 237–260
- (with Yuxin Ge, Jie Wu) A new mass for asymptotically flat manifolds, arXiv:1211.3645 Adv. Math. 266 (2014), 84–119.
- (with Yong Luo) On geometrically constrained variational problems of the Willmore functional I: the Lagrangian Willmore problem. Comm. Aanl and Geom., 23 (2015)191-223
- (with Q. Chen, J. Jost) A maximum principle for generalizations of harmonic maps in Hermitian, affine, Weyl, and Finsler geometry, J. Geom. Anal. 25 (2015), no. 4, 2407-2426 (with Yuxin Ge, Jie Wu) Hyperbolic Alexandrov-Fenchel quermassintegral inequalities I arXiv:1303.1714, unpublished
- (with Y. Ge and J. Wu) The GBC mass for asymptotically hyperbolic manifolds The GBC mass for asymptotically hyperbolic manifolds, Math. Z. 281 (2015), no. 1-2, 257–297. (Its announcement published in C. R. Math. Acad. Sci. Paris 352 (2014), no. 2, 147–151. )
- (with Y. Ge, J. Wu and C. Xia) A Penrose inequality for graphs over Kottler space, arXiv:1309.6248, Calc. PDE 52 (2015), no. 3-4, 755–782.
- Jin, Yan; Jost, Jürgen; Wang, Guofang A new nonlocal variational setting for image processing. Inverse Probl. Imaging 9 (2015), no. 2, 415–430.
- Chen, Li; Wang, Guofang, σ2-diffeomorphisms between 4-dimensional annuli. Calc. Var. Partial Differential Equations 55 (2016), no. 3, Art. 49, 20 pp
- Ge, Yuxin; Wang, Guofang; Wu, Jie; Xia, Chao Gauss-Bonnet-Chern mass and Alexandrov-Fenchel inequality. Front. Math. China 11 (2016), no. 5, 1207–1237.
- Wang, G; Wu, Jie Chern's magic form and the Gauss-Bonnet-Chern mass. Math. Z. 287 (2017), no. 3-4, 843–854.
- Bauer, Frank; Hua, Bobo; Jost, Jürgen; Liu, Shiping; Wang, G., The geometric meaning of curvature: local and nonlocal aspects of Ricci curvature. Modern approaches to discrete curvature, 1–62, Lecture Notes in Math., 2184, Springer, Cham, 2017
- Han, Qing; Wang, G.,Hessian surfaces and local Lagrangian embeddings. Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 3, 675–685.
- Wang, Guofang; Xia, Chao Uniqueness of stable capillary hypersurfaces in a ball. Math. Ann. 374 (2019), no. 3-4, 1845–1882.
- Wang, Guofang; Weng, Liangjun A mean curvature type flow with capillary boundary in a unit ball. Calc. Var. Partial Differential Equations 59 (2020), no. 5, Paper No. 149, 26 pp.
- Li, Mingyan; Wang, Guofang; Weng, Liangjun Lagrangian surfaces with Legendrian boundary. Sci. China Math. 64 (2021), no. 7, 1589–1598.
- Guo, Jinyu; Wang, Guofang; Xia, Chao Stable capillary hypersurfaces supported on a horosphere in the hyperbolic space. Adv. Math. 409 (2022), part A, Paper No. 108641, 25 pp
- Scheuer, Julian; Wang, Guofang; Xia, Chao Alexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ball. J. Differential Geom. 120 (2022), no. 2, 345–373.
- X. Mei, G.Wang, Liangjun Weng “A Constrained Mean Curvature Flow and Alexandrov–Fenchel Inequalities,” International Mathematics Research Notices, pp 1–23 https://doi.org/10.1093/imrn/rnad020
- Guofang Wang · Liangjun Weng · Chao Xia, Alexandrov–Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary, Math. Ann, https://doi.org/10.1007/s00208-023-02571-4
- G. Wang, Chao Xia, Guan-Li type mean curvature flow for free boundary hypersurfaces in a ball, arXiv:1910.07253 to appear in CAG

To the Analysis Group.