Complete surfaces in homogeneous spaces with constant mean curvature

Author(s)

Aires Eduardo Menani Barbieri

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2024-02-09

Examining board members

Fernando Manfio; Ruy Tojeiro de Figueiredo Junior; Jose Maria Espinar Garcia; Maria Asuncion Jimenez Grande

• Advisor: Fernando Manfio

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 work we 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. (AU)

• FAPESP's process: 21/05766-8 - Complete surfaces in homogeneous spaces with constant mean curvature
• Grantee: Aires Eduardo Menani Barbieri
• Support Opportunities: Scholarships in Brazil - Master