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Workgroup Applied Analysis

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 2.029

Address
Englerstrasse 2
76131 Karlsruhe

Contact by E-Mail is quick and sure: kaori.nagatou@kit.edu
(Dr. Kaori Nagato-Plum)

-----------------------------

Office hours:
Mo. -- Fr. 10:00-12:00

Tel.: +49 721 608 42056

Fax.: +49 721 608 46214

GAFKA

15.06.2016 in Karlsruhe (SR 1.067)

  • 16:00-17:00: Armin Schikorra (Freiburg): Ohara's knot energies and W^{1/p,p}-harmonic maps into spheres
  • 17:15-18:15: Burkhard Wilking (Münster): Positively curved manifolds under logarithmic symmetry assumptions

Abstract: We show that the Euler characteristic of a positively curved n manifold M coincides with the Euler characteristic of an n-dimensional compact rank 1 symmetric space provided that the rank
of the isometry group of M is larger than 3log_2n.

24.06.2015 in Frankfurt

  • 16:15-17:15: Carlo Sinestrari (Rom): Volume preserving flow of convex hyper surfaces by powers of the mean curvature
  • 17:45-18:45: Theodora Bourni (Berlin): Null mean curvature flow and marginally outer trapped surfaces

10.12.2014 in Karlsruhe (Redtenbacher Hörsaal)

  • 14:45-15:45: Urs Lang (Zürich): Local currents in metric spaces and applications to asymptotic geometry

Abstract: The talk will first review (a local variant of) the Ambrosio-Kirchheim theory of currents in
metric spaces. A central role is played by various notions of convergence and compactness
theorems for locally integral currents. Then some isoperimetric inequalities in spaces of nonpositive
curvature and applications to the asymptotic geometry of such spaces will be discussed.
(This is partly joint work with Stefan Wenger and with Bruce Kleiner.)

  • 15:45-16:15 Coffee
  • 16:15-17:15: Gerhard Huisken (Tübingen / MFO): Mean curvature flow with surgery

Abstract: The evolution of a hypersurface along its mean curvature vector
in a Riemannian manifold typically encounters highly complicated singularities
that are understood only in certain cases. The lecture describes joint work with
Simon Brendle classifying all singularities of mean-convex embedded solutions
of mean curvature flow in the 2-dimensional case. Using new non-collapsing
and pseudolocality estimates it is shown that the flow can be extended
with finitely many surgeries until the solution either vanishes or converges to
a minimal surface.

26.11.2014 in Frankfurt

  • Manuel del Pino (Santiago): Variations on the Bombieri-De Giorgi-Giusti minimal graph
  • Emanuele Spadaro (Leipzig): An improved estimate of the singular set of Dir-minimizing multiple valued functions

09.07.2014 in Karlsruhe

  • 16:00-17:00 Miles Simon (Magdeburg): Ricci flow of regions with curvature bounded below in dimension three

Abstract: We consider smooth complete solutions to Ricci flow with bounded
curvature on manifolds without boundary in
dimension three. Assuming a
ball at time zero of radius one has curvature bounded from below by -1, then
we prove estimates which show that compactly contained subregions of
this ball will be smoothed out by the Ricci flow for a short but well
defined time interval.
The estimates we obtain depend on the initial volume of the ball and
the distance from the compact region to the boundary of the initial
ball. They do not depend on the upper bound of the curvature on the ball at time zero.
Versions of these estimates for balls of radius r follow using
scaling arguments.

  • 17:30-18:30 Anton Petrunin (Penn State): Smoothing and Faceting

Abstract: I will discuss bilateral approximations and related curvature conditions
between Riemannian and Polyhedral spaces.

07.05.2014 in Frankfurt

  • 16:00-17:00 Melanie Rupflin (Leipzig): Global solutions of Teichmüller harmonic map flow
  • 17:30-18:30 Andrea Mondino (Zürich): Some analytic and geometric properties of metric measure spaces with lower Ricci curvature bounds