Seminars summer 2015
There are several research seminars in the PotsdamBerlin area which are closely related to Geometric Analysis:
 Usually biweekly during term, on Thursdays, the joint seminar "Topics in Geometric Analysis" taking place in turns at the University of Potsdam (UP), the Albert Einstein Institute (AEI) and the Free University Berlin (FU). It is organised by Theodora Bourni (FU), Ulrich Menne (AEI), and Jan Metzger (UP). The dates are Apr 23 (UP), May 7 (FU), May 21 (AEI), Jun 4 (UP), Jun 18 (FU) and Jul 2 (AEI).
 In the weeks where there is no "Topics in Geometric Analysis" seminar there will usually be a reading seminar on "Geometric Measure Theory" at the Albert Einstein Institute (AEI). It will take place on Apr 16, Apr 30, May 28, Jun 11, Jun 25, Jul 7, and Jul 16. Details see below.
Dates  Type  Place  Speaker  Topic 

Apr 16th, 2015, 09:4511:30  GMT reading seminar  Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam  Theodora Bourni (FU Berlin)  Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981. 
Apr 16th, 2015, 12:3013:45  GMT reading seminar  Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam  Theodora Bourni (FU Berlin)  Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981. 
Apr 23th, 2015, 16:1517:15  Topics in Geometric Analysis  University of Potsdam, Room 1.15, Building 9, Am Neues Palais 10, 14469 Potsdam  Manuel Ritoré (Universidad de Granada) 
Isoperimetric inequalities in unbounded convex bodies I shall consider the problem of minimizing the relative perimeter under a volume constraint in the interior of an unbounded convex body with arbitrary boundary. I shall give an example of a convex body whose isoperimetric profile is identically zero and give a characterization of the convex bodies with positive isoperimetric profile in terms of their asymptotic cylinders. I shall also show existence of isoperimetric regions in a generalized sense, and prove the concavity of the function I^{(n+1)/n}, where I is the isoperimetric profile and R^{n+1} is the ambient Euclidean space. This is joint work in progress with Gian Paolo Leonardi and Efstratios Vernadakis. 
Apr 23th, 2015, 17:4518:45  Topics in Geometric Analysis  University of Potsdam, Room 1.15, Building 9, Am Neues Palais 10, 14469 Potsdam  Julian Scheuer (Universität Freiburg)  Explicit rigidity for almostumbilical hypersurfaces 
Apr 30th, 2015, 09:4511:30  GMT reading seminar  Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam  Theodora Bourni (FU Berlin)  Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981. 
Apr 30th, 2015, 12:3013:45  GMT reading seminar  Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam  Theodora Bourni (FU Berlin)  Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981. 
May 7th, 2015, 16:1517:15  Topics in Geometric Analysis  FU Berlin, Room 007/008, Arnimallee 6, 14195 Berlin  Tristan Rivière (ETH Zürich) 
Some results on the calculus of variations of Riemann surfaces We shall present various aspects of the minimization of functionals for immersion into the spheres of surfaces under constrained conformal class. We will focus in particular on the variations of the Willmore and the area functional in the class of weak conformal immersions of given Riemann surfaces. We will in particular give a characterization of riemann tori into S3 minimizing locally the conformal volume. 
May 7th, 2015, 17:4518:45  Topics in Geometric Analysis  FU Berlin, Room 007/008, Arnimallee 6, 14195 Berlin  Benjamin Sharp (Imperial College London) 
Compactness theorems for minimal hypersurfaces with bounded index I will present a new compactness theorem for minimal hypersurfaces embedded in a closed Riemannian manifold N^{n+1} with n<7. When n=2 and N has positive Ricci curvature, Choi and Schoen proved that a sequence of minimal hypersurfaces with bounded genus converges smoothly and graphically to some minimal limit. A corollary of our main theorem recovers the result of ChoiSchoen and extends this appropriately for all n<7.

May 21st, 2015, 16:1517:15  Topics in Geometric Analysis  Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam  Lu Wang (Imperial College London) 
A Topological Property of Asymptotically Conical Selfshrinkers with Small Entropy For any asymptotically conical selfshrinker with entropy less than or equal to that of a cylinder we show that the link of the asymptotic cone must separate the unit sphere into exactly two connected components, both diffeomorphic to the selfshrinker. Combining this with recent work of Brendle, we conclude that the round sphere uniquely minimizes the entropy among all nonflat twodimensional selfshrinkers. This confirms a conjecture of ColdingIlmanenMinicozziWhite in dimension two. 
May 21st, 2015, 17:4518:45  Topics in Geometric Analysis  Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam  Martin Meurer (RWTH Aachen) 
Integral Menger Curvature and Rectifiability of $n$dimensional Borel sets in Euclidean $N$space In 1999 J.C. Léger proved that a onedimensional set with finite total Menger curvature is 1rectifiable. In this talk we will present a generalisation of this result to sets of arbitrary dimension and codimension. We will give a short sketch of the proof and discuss different higher dimensional versions of Menger curvature known from the literature. 
May 28th, 2015, 09:4511:30  GMT reading seminar  Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam  Anna Sakovich (AEI)  Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981. 
May 28th, 2015, 12:3013:45  GMT reading seminar  Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam  Anna Sakovich (AEI)  Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981. 
Jun 4th, 2015, 16:1517:15  Topics in Geometric Analysis  University of Potsdam, Room 1.15, Building 9, Am Neues Palais 10, 14469 Potsdam  Benjamin Lambert (Universität Konstanz) 
Inverse Mean Curvature Flow inside the Sphere Usually the inverse mean curvature flow (IMCF) of convex hypersurfaces exists for all time and flows outwards towards infinitely large spheres. In this talk we will consider IMCF on of convex disks inside the unit ball with a Neumann boundary condition on the sphere. We will see that conversely to the boundaryless case, global singularities occur in finite time, and the flow converges in C^{1, \beta} to a flat disk. 
Jun 4th, 2015, 17:4518:45  Topics in Geometric Analysis  University of Potsdam, Room 1.15, Building 9, Am Neues Palais 10, 14469 Potsdam  Simone Di Marino (Université ParisSud) 
Sobolev spaces on metric measure spaces via derivations and integration by parts formula I will illustrate recent developments of the theory of Sobolev spaces on metric measure spaces. In particular I will focus on the more recent viewpoint, inspired by Weaver’s derivations, which provides an integration by parts formula even in the abstract setting. I will show how this viewpoint is completely equivalent to the usual one constructed by approximation with Lipschitz functions under very mild assumptions on the metric measure structure. If there is time I will discuss also the theory for BV and $W^{1,1}$ spaces. 
Jun 11th, 2015, 09:4511:30  GMT reading seminar  Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam  Anna Sakovich (AEI)  Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981. 
Jun 11th, 2015, 12:3013:45  GMT reading seminar  Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam  Anna Sakovich (AEI)  Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981. 
Jun 18th, 2015, 16:1517:15  Topics in Geometric Analysis  FU Berlin, Room 007/008, Arnimallee 6, 14195 Berlin  Peter Topping (University of Warwick) 
Refined asymptotics of the Teichmueller harmonic map flow I will give an introduction to the Teichmueller harmonic map flow, which is related both to the harmonic map flow and the mean curvature flow. I will describe some work, completed earlier this year, establishing that the large time effect of the flow is to decompose the flow map into branched minimal immersions with no loss of energy. Joint work with Tobias Huxol, Melanie Rupflin and Miaomiao Zhu. 
Jun 18th, 2015, 17:4518:45  Topics in Geometric Analysis  FU Berlin, Room 007/008, Arnimallee 6, 14195 Berlin  Debora Impera (Università degli Studi di MilanoBicocca) 
Rigidity results and topology at infinity of translating solitons of the mean curvature flow In this talk I will discuss some rigidity results and obstructions on the topology at infinity of translating solitons of the mean curvature flow in the Euclidean space. These results were recently obtained in collaboration with M. Rimoldi and our approach relies on the theory of fminimal hypersurfaces. 
Jun 25th, 2015, 09:1511:30  GMT reading seminar  Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam 
Anna Sakovich (AEI) 
Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981. 
Jun 25th, 2015, 12:3013:45  GMT reading seminar  Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam  Anna Sakovich (AEI)  Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981. 
Jul 2nd, 2015, 16:1517:15  Topics in Geometric Analysis  Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam  Ye Sle Cha (FU Berlin) 
Geometric Inequalities in General Relativity for NonMaximal Initial Data The geometric inequalities (Penrose Inequalities) in general relativity which relate to the ADM mass, angular momentum and charge have been proven for a large class of the axially symmetric, asymptotically flat, maximal initial data of the EinsteinMaxwell equations. In this talk, we will introduce how to reduce the general formulation for the nonmaximal initial data, to the known maximal case, whenever a system of elliptic equations admits a solution. Each equation in the system will be analyzed individually, and the solvability of the system in the near maximal case will be discussed. The talk is based on joint work with Marcus Khuri. 
Jul 2nd, 2015, 17:4518:45  Topics in Geometric Analysis  Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam  Melanie Rupflin (Universität Leipzig) 
Horizontal curves of metrics and applications to geometric flows The evolution of a family of metrics on a closed surface can always be described as a combination of a conformal change, a change obtained by pulling back with suitable diffeomorphisms and an evolution in "horizontal direction". As we shall discuss in this talk, curves that move only in horizontal direction turn out to be very well controlled even when the underlying conformal structure degenerates. As an application we will show that solutions of Teichmüller harmonic map flow can be continued canonically past any finite time singularity and consequently that this flow admits global weak solution for arbitrary initial data and target manifolds. Joint work with Peter Topping. 
Jul 9th, 2015, 09:4511:30  GMT reading seminar  Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam 
Ulrich Menne (AEI) 
Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981. 
Jul 9th, 2015, 12:3013:45  GMT reading seminar  Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam 
Ulrich Menne (AEI) 
Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981. 
Jul 16th, 2015, 09:4511:30  GMT reading seminar  Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam  Ulrich Menne (AEI)  Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981. 
Jul 16th, 2015, 12:3013:45  GMT reading seminar  Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam  Ulrich Menne (AEI)  Richard Schoen and Leon Simon, "Regularity of Stable Minimal Hypersurfaces", 1981. 
Jul 23th, 2015, 09:4511:30  GMT reading seminar  Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam  Mario Santilli (AEI)  Herbert Federer, "Geometric Measure Theory", 1969: 5.4.115.4.14. 
Jul 23th, 2015, 12:3013:45  GMT reading seminarsa  Albert Einstein Institute, Room 0.01, Am Mühlenberg 1, 14476 Potsdam  Mario Santilli (AEI)  Herbert Federer, "Geometric Measure Theory", 1969: 5.4.115.4.14. 