Oberseminar Prof. Dr. B. Wilking/Prof. Dr. C. B&ooum;hm

Minimax minimal surfaces and positive scalar curvature

Classical results in Differential Geometry show that the scalar curvature controls the topology of area-minimizing surfaces. In this talk I will explain what happens if the surface is not area-minimizing but comes form a min-max method. This is joint work with F. Marques.

Expanding solitons with non-negative curvature operator coming out of
cones"

We show that a Ricci flow of any complete Riemannian manifold without
boundary with bounded non-negative curvature operator and non-zero
asymptotic volume ratio exists for all time and has constant asymptotic volume ratio.
We show that there is a limit solution, obtained by scaling down this
solution at a fixed point in space, which is an expanding soliton coming
out of the asymptotic cone at infinity.

Datum	Vortragender	Titel
04.04.2011	Nikolai Nowaczyk
18.04.2011	Stephan Huckemann	Statistics on manifolds
02.05.2011	Vicente Cortés Universität Hamburg	Complete quaternionic Kähler manifolds associated to cubic polyomials
09.05.2011	Robert Haslhofer ETH Zürich	Singularities in 4d Ricci flow Ricci flow in higher dimensions without curvature assumptions inevitably leads to the formation of intriguingly complex singularities. To shed some light on that, I will describe a general compactness theorem for the space of singularity models in arbitrary dimensions, and a specially powerful compactness theorem in dimension four. I will also sketch a bigger picture about high curvature regions in 4d Ricci flow. This is a joint work with Reto Mueller.
16.05.2011	Carla Cederbaum MPG Berlin	The Newtonian Limit of Geometrostatics Geometrostatics is the geometric theory of static isolated relativistic systems modeling for example static stars or black holes in our universe. It is governed by a system of (mainly) elliptic PDEs relating a $3$-dimensional Riemannian metric and a positive function describing the geometry of space at any given point of time and the passage of time, respectively. While these PDEs have been intensively studied in the last century from both analytic and physical viewpoints, their geometric nature had not been exploited to its full extent. We will present a number of new insights into geometrostatics that mainly rely on a geometric approach but are also interrelated with analytic and physical aspects of the theory. For example, we will discuss geodesics of the corresponding Lorentzian spacetimes, uniqueness questions, mass and center of mass of geometrostatic systems, and last but not least their Newtonian limit -- the question of whether and how these relativistic systems have Newtonian counterparts.
23.05.2011	Andre Neves Imperial College London	Minimax minimal surfaces and positive scalar curvature Classical results in Differential Geometry show that the scalar curvature controls the topology of area-minimizing surfaces. In this talk I will explain what happens if the surface is not area-minimizing but comes form a min-max method. This is joint work with F. Marques.
30.5.2011	Miles Simon	Expanding solitons with non-negative curvature operator coming out of cones" We show that a Ricci flow of any complete Riemannian manifold without boundary with bounded non-negative curvature operator and non-zero asymptotic volume ratio exists for all time and has constant asymptotic volume ratio. We show that there is a limit solution, obtained by scaling down this solution at a fixed point in space, which is an expanding soliton coming out of the asymptotic cone at infinity.
06.06.2011	Lars Schäfer Universität Hannover	On the HSL-Flow Abstract: We introduce a natural geometric fourth order flow associated to Hamiltonian stationary sub-manifolds in Kaehler-Einstein manifolds. Afterwards we discuss some of its properties, short-time existence and give existence-time estimates of the initial geometry.
20.06.2011	Tobias Lamm Universität Frankfurt a.M.	Superquadratic curvature functionals for immersed surfaces Abstract: We introduce superquadratic curvature functionals involving the mean curvature and second fundamental form of immersed surfaces. We prove the existence and regularity of critical point of these functionals and we show that the Palais-Smal condition holds. This is a joint work with Ernst Kuwert and Yuxiang Li.
27.06.2011	Stephan Wiesendorf Universität Köln	Singular Riemannian foliations with taut leaves Singular Riemannian foliations occur naturally in Riemannian geometry as the generalization of the partition of a Riemannian manifold into the orbits of an isometric group ation. In this talk we consider a singular Riemannian foliation, such that all of its leaves are taut submanifolds, where we call a submanifold taut if the energy functional on a generic homotopy fiber of the inclusion is a perfect Morse function, and show that this property only depends on the horizontal geometry of the foliation, thus it can be read off the quotient and vice versa.
04.07.2011	Carlo Mantegazza, SNS Pisa	Flow by mean curvature inside a moving ambient space I will discuss some computations related to the motion by mean curvature of a submanifold inside an ambient Riemannian manifold evolving by Ricci or backwards Ricci-flow. Special emphasis will be put on the generalization of Huisken´s monotonicity formula and its connection with the validity of some Li-Yau-Hamilton-type inequalities in a moving manifold.
11.07.2011	Michael Struwe ETH Zürich	Quantization in Geometric Analysis Geometric variational problems are characterized by scale invariance and therefore often lack the compactness properties required for the use of variational methods. The discovery of threshold phenomena and, in fact, quantization of the energy levels where compactness fails lead to the resolution of a number of classical conjectures in Geomeric Analysis, such as Rellich's conjecture or convergence of the Yamabe flow. In my talk I will survey some of these results and conclude with recent quantization results for the class of elliptic equations related to the Moser-Trudinger-Adams inequality in a "super-critical" regime, whose concentration behavior is governed by a geometric "limit equation

Arbeitsgruppe Differentialgeometrie
(Prof. Dr. B. Wilking, Prof. Dr. C. Böhm)

Vorträge im Oberseminar Differentialgeometrie, SS 2011

Arbeitsgruppe Differentialgeometrie (Prof. Dr. B. Wilking, Prof. Dr. C. Böhm)

Vorträge im Oberseminar Differentialgeometrie, SS 2011

Arbeitsgruppe Differentialgeometrie
(Prof. Dr. B. Wilking, Prof. Dr. C. Böhm)