Oberseminar Analysis, Geometrie und Physik
Freie Universität Berlin - Fachbereich Mathematik und Informatik
Arnimallee 2-6, 14195 Berlin-Dahlem (Raum 032)
Sommersemester 2005, Dienstag 17.15 Uhr

Veranstalter:
-- Prof. Dr. Klaus Ecker (FU Berlin)
-- Prof. Dr. Gerhard Huisken (MPI Gravitationsphysik Golm/FU Berlin)
-- Julie Clutterbuck (FU Berlin), Gruppe Geometric Analysis.

12.4.2005: Klaus Ecker
Local monotonicity formula for Ricci flow
19.4.2005: SFB Colloquium

26.4.2005: Oliver Schnürer
Konvexe Funktionen und im Unendlichen abfallende Lösungen (Convex Functions and Solutions Decaying at Infinity)
Im ersten Teil des Vortrages zeigen wir, dass es nur auf konvexen Mengen konvexe Funktionen gibt, deren Gradient am Rand unbeschränkt wird.
Im zweiten Teil betrachten wir Lösungen einer linearen Wärmeleitungsgleichung mit Gradiententermen. Hier interessieren wir uns für Bedingungen an die Gradiententerme, die Lösungen, die anfangs im Unendlichen abfallen, im Unendlichen in unendlicher Zeit abheben lassen. (Projekt mit Hartmut Schwetlick)
3.5.2005: Daniel John (Ruhr-Universität Bochum)
The isoperimetric problem in symmetric spaces of noncompact type
Symmetrization procedures have been a basic tool in the history of the isoperimetric problem in constant curvature spaces. In this talk we present a new symmetrization procedure for domains in symmetric spaces of noncompact type. This symmetrization generalizes the well known Steiner symmetrization in euclidean space. In contrast to the classical construction the symmetrized domain is obtained by solving a nonlinear elliptic equation of mean curvature type. So far, it is not possible to solve the isoperimetric problem in symmetric spaces of noncompact type by applying this symmetrization procedure. Nevertheless, it provides some interesting insights into the qualitative behavior of isoperimetric solutions.
10.5.2005: SFB Colloquium

17.5.2005: Friedrich Tomi (Universität Heidelberg)
The Barrier Principle for Minimal Submanifolds of Arbitrary Codimension and Applications
A hypersurface B in some n-dimensional Riemannian manifold N is called k-mean-convex with respect to a unit normal vector field &nu, if the sum of the k smallest principal curvatures of B in direction &nu is nonnegative, 1 &le k < n. This generalizes the familiar notion of mean convexity in the case k=n-1. An application of Hopf's maximum principle yields the following:
Barrier Principle. Let B &sub N be k-mean convex and let M &sub N be a k-dimensional minimal surface which touches B in some point p &isin B from the k-mean convex side of B. Then it follows that M &cap U &sub B for some neighborhood U of p.
If one can construct suitable such barriers these may be exploited in existence theorems for minimal surfaces to force specified geometric and topological properties upon these surfaces. We give such applications in the exterior Plateau problem. Complete abstract here.
24.5.2005: Josh Bode
Gradient estimates on cylindrical graphs evolving under mean curvature flow
31.5.2005: SFB Colloquium

7.6.2005: Natasa Sesum (Courant Institute)
The compactness result for Kähler Ricci solitons
14.6.2005: Darya Apushkinskaya (Universität des Saarlandes)
Regularity of free boundaries in parabolic obstacle type problems
21.6.2005: SFB Colloquium

28.6.2005: SFB Colloquium

4.7.2005, 12.15 Uhr
Joel Smoller: Rotating fluids with self-gravitation in bounded domains
Please note this is on a Monday!
5.7.2005: Jörg Härterich
Front motion in multi-dimensional viscous balance laws
12.7.2005: SFB Colloquium

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