Seminár 3.11.2011: Daniel Ševčovič (FMFI)

[sevcovic]

Štvrtok 3.11.2011, 14:30-15:30, F1-326 / Thursday, October 20, 2011, 2:30-3:30 PM, F1-326

Daniel Ševčovič (FMFI Univerzita Komenského Bratislava)

On a gradient flow for the anisotropic ratio and other nonlocal geometric flows


Abstrakt/Abstract:

We analyze a geometric flow of closed curves in the plane minimizing
the anisoperimetric ratio. For such a flow the normal velocity is a
function of the curvature and it also depends on the total interfacial
energy and enclosed area of the curve. We show that there exist initial
curves for which the enclosed area is decreasing with respect to time.
This is in contrast to the gradient flow minimizing the isoperimetric
ratio. We also derive a mixed anisoperimetric inequality for the product
of total interfacial energies corresponding to different anisotropy
functions. Finally, we present several computational examples
illustrating theoretical results.


Najbližší program / Near future program:
10.11. Matthias Wolfrum (WIAS Berlin)
17.11. sviatok
24.11. Eiji Yanagida (Tokyo Institute of Technology)