Geometrial and analytical aspects of constant mean curvature immersions
Biharmonic surfaces in three-dimensional Riemannian manifolds
Triply periodic constant mean curvature surfaces in the hyperbolic space
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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