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Complete surfaces in homogeneous spaces with constant mean curvature

Grant number: 21/05766-8
Support Opportunities:Scholarships in Brazil - Master
Effective date (Start): August 01, 2021
Effective date (End): January 31, 2024
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Fernando Manfio
Grantee:Aires Eduardo Menani Barbieri
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):22/14381-5 - Elliptic special Weingarten surfaces of minimal type in the homogeneous space E(k,t), BE.EP.MS

Abstract

The theory of minimal surfaces, and more generally, constant mean curvature surfaces in the 3-dimensional Euclidean space has its roots in the calculus of variations developed by Euler and Lagrange in the 18th century and in later investigations by Enneper, Riemann, Weierstrass, among others, in the 19th century. Many of the global questions and conjectures that arose in this classical subject have only recently been addressed. In this research project we will study some results on complete surfaces of constant mean curvature in the three-dimensional Euclidean space and, more generally, in homogeneous three-dimensional spaces, whose Gaussian curvature does not change sign.

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Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
BARBIERI, Aires Eduardo Menani. Complete surfaces in homogeneous spaces with constant mean curvature. 2024. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.

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