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Uniqueness of immersed spheres in three-dimensional Riemannian manifolds and Enneper-type hypersurfaces

Grant number: 20/03431-6
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): August 01, 2020
Effective date (End): July 31, 2022
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Ruy Tojeiro de Figueiredo Junior
Grantee:Marcos Paulo Tassi
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Associated research grant:16/23746-6 - Algebraic, topological and analytical techniques in differential geometry and geometric analysis, AP.TEM

Abstract

Part of our project consists in the study of general hypotheses on a certain class of surfaces in order to guarantee uniqueness of spheres immersed in three-dimensional Riemannian manifolds, in the sense of the generalized version of Hopf's Theorem proved by J.A. Gálvez and P. Mira (Uniqueness of immersed spheres in three-manifolds, to appear in Journal of Differential Geometry). We also intend to investigate Enneper-type (in particular, Joachimsthal-type) hypersurfaces with relevant geometric properties, according to the explicit description of such hypersurfaces recently obtained by S. Chión and R. Tojeiro, in 2020. (AU)