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Prescribed curvature measure problem in hyperbolic space

Fengrui Yang (McGill, Canada)

Dienstag, 26. Januar 2021 15:00Uhr

The problem of the prescribed curvature measure is one of the important problems in differential geometry and nonlinear partial differential equations. In this talk, we are going to talk about our recent result about prescribed curvature measure problem in hyperbolic space.We obtained the existence of star-shaped k-convex bodies with prescribed (n-k)-th curvature measures (k<n) by establishing crucial C^2 regularity estimates for solutions to the corresponding fully nonlinear PDE in the hyperbolic space.