Freie Universität Berlin -
Fachbereich Mathematik und Informatik
Arnimallee 2-6,
14195 Berlin-Dahlem
(Raum 032)
Sommersemester 2005, Dienstag 17.15 Uhr
12.4.2005:
Klaus Ecker
Local monotonicity formula for Ricci flow
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.
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
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
4.7.2005, 12.15 Uhr
Joel Smoller: Rotating fluids with self-gravitation in bounded domains
Please note this is on a Monday!
Front motion in multi-dimensional viscous balance laws
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Sommersemester 2004
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