Topics in Geometric Analysis

26.11.2019, 16:15-18:45  –  FU Berlin, Arnimallee 6, SR 031
Seminar "Topics in Geometric Analysis"

Esko Heinonen, Nicolas Marque

16:15Esko Heinonen

Jenkins-Serrin problem for translating graphs

A translating soliton is a smooth oriented hypersurface S in MxR (or in Rn+1) whose mean curvature satisfies H = <X,N>, where X is a given vector and N denotes the unit normal to the surface S. In the case S is a graph of a function u, u satisfies the so-called translating soliton equation and S will be called a translating graph. These solitons play an important role in the study of the singularities of the mean curvature flow, but recently they have gained also a lot of interest on their own.

On the other hand, the Jenkins-Serrin problem asks for solutions (of certain PDE) to a Dirichlet problem on a domain D such that the boundary data can be also infinite on some parts of the boundary of D. This problem has been considered earlier e.g. for the minimal surfaces but in this talk I will discuss about existence results for the translating soliton equation in Riemannian products MxR. The talk is
based on recent joint works with E.S. Gama, J. de Lira and F. Martín.

17:45Nicolas MarqueCompactness of Willmore immersions
The Willmore energy naturally arises as an elastic energy measuring how curved an immersed surface is. Its critical points are called Willmore surfaces, and sequences of Willmore surfaces are subject to concentration-compactness phenomena, and thus to bubbling. After detailing the formation of Willmore bubble trees, I will explore the specific case of simple minimal bubbles and detail its consequences on the compactness of Willmore immersions, depending on their energy.

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