summer 2018 



Daniel Ballesteros Chavez, Politechnika Poznańska 15.11.2023 13:00, B137 Title: A curvature estimate for the Weyl problem in de Sitter space
The problem of isometric embedding of a positively curved 2sphere in the Euclidean 3space was considered by Hermann Weyl in 1916 and it's known as the classical Weyl problem. In this talk we will give an overview of L. Nirenberg's solution to this problem and where curvature estimates are needed. Then we will consider the existence of (spacelike) isometric embeddings of a metric on the sphere into de Sitter space, with a suitable curvature restriction. We show a bound for the mean curvature H of such spacelike hypersurfaces in terms of the scalar curvature, its Laplacian, the dimension and a scaling factor of the ambient space. The proof uses geometric identities, and the maximum principle for a prescribed symmetriccurvature equation.This is joint work with Ben Lambert and Wilhelm Klingenberg.


Last modified: 16.11.2022 