5. FHSTMeeting on Geometry and Analysis
FreiburgHeidelbergStuttgartHeidelberg


Anna Dall'Acqua: On the Willmore flow of tori or revolution
In this talk we present a stricking relationship between Willmore surfaces of revolution and elastic curves in hyperbolic halfspace. Here the term elastic curve refer to a critical point of the energy given by the integral of the curvature squared. In the talk we will discuss this relationship and use it to study longtime existence and asymptotic behavior for the L^2gradient flow of the Willmore energy, under the condition that the initial datum is a torus of revolution. As in the case of Willmore flow of spheres, we show that if an initial datum has Willmore energy below 8 \pi then the solution of the Willmore flow converges to the Clifford Torus, possibly rescaled and translated. The energy threshold of 8 \pi turns out to be optimal for such a convergence result.
The lecture is based on joint work with M. Müller (Univ. Leipzig), R. Schätzle (Univ. Tübingen) and A. Spener (Univ. Ulm).
Marius Müller: Embeddednessbreaking of elastic flows
This talk is based on a joint work with T.Miura (Tokyo) and F. Rupp (Vienna).
We study the qualitative behavior of elastic flows of closed curves, i.e. L2gradient evolutions of the EulerBernoulli elastic energy.
We are interested in the question of embeddednesspreservation  Can the evolution of an embedded curve develop selfintersections?
In general the answer is 'no', as shown by S. Blatt (2010) for a large class of fourth order geometric flows. We can however expose an (optimal) energy threshold under which evolutions still preserve embeddedness.
The optimal threshold has a geometric significance. To understand it we will enter the fantastic world of Euler's elastic curves.
Alex Waldron: Finitetime singularities of 2D harmonic map flow
I'll discuss recent work on continuity of the body map at finitetime singularities of 2D harmonic map flow, assuming the initial data is almostholomorphic (in the energy sense) or the blowup is "strictly typeII." This is relevant to a conjecture of Topping. Time permitting, I'll also discuss uniqueness of subsequential limits at infinite time.
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