SEMINARIO DI EQUAZIONI DIFFERENZIALI
Dipartimento di Matematica
Università degli Studi di Roma "Tor Vergata"
Tuesday 5th December, 16:00, Aula Dal Passo
Speaker: Liangjun Weng (Università di Roma "Tor Vergata")
Title: The capillary Minkowski problem
Abstract: The classical Minkowski problem asks for necessary and sufficient conditions on a non-negative Borel measure on the unit sphere to be the surface area measure of a convex body. In a smooth setting, it reduces to the study of a Monge-Ampere equation on the unit sphere. This problem has been completely solved through the seminal works of Nirenberg, Pogorelov, Cheng-Yau, etc. In this talk, a new Minkowski-type problem will be introduced. The problem asks for the existence of a convex hypersurface with prescribed Gauss-Kronecker curvature and capillary boundary supported on an obstacle, which can be deduced as a Monge-Ampere equation with a Robin (or Neumann) boundary value condition on the spherical cap. Then obtain a necessary and sufficient condition for solving this problem.
NB: This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006
Website:
http://www.mat.uniroma2.it/~ricerca/analis/Seminario%20di%20Equazioni%20Differenziali.html--
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