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)