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

• Grant number: 20/03431-6
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2020
• End date: October 29, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ruy Tojeiro de Figueiredo Junior
• Grantee: Marcos Paulo Tassi
• Host 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
• Associated scholarship(s): 21/10181-9 - Joachimsthal surfaces with nonzero constant Gaussian curvature, BE.EP.PD

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)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

GALVEZ, JOSE A.; MIRA, PABLO; TASSI, MARCOS P.. A quasiconformal Hopf soap bubble theorem. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, v. 61, n. 4, p. 20-pg., 2022-08-01. (20/03431-6)