Weingarten Surfaces, Self-Shrinkers and Hyperbolic Surfaces

• Grant number: 18/03721-4
• Support Opportunities: Regular Research Grants
• Duration: June 01, 2018 - May 31, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Alexandre Paiva Barreto
• Grantee: Alexandre Paiva Barreto
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

This research project concerns Riemannian surfaces and it is divided into three parts..In the first part of the project we are interested in studying Weingarten surfaces, that is, surfaces whose principal curvatures verify a certain relation (generally polynomial) over the entire surface. In the second part of the project we are interested in studying self-shrinkers surfaces that appear when we study the singularities of the mean curvature flow. In both of these parts, our main goal is to classify the surfaces with constant length of the second fundamental form.The third and final part of the project aims to develop a computational study of the Fuchsian groups and their Dirichlet's domains. We will use the results obtained to determine topological invariants of hyperbolic surfaces/orbifolds and study their deformations (this part is reminiscent of the previous regular design). (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)

BARRETO, ALEXANDRE P.; COSWOSCK, FABIANI A.; HARTMANN, LUIZ. Curvature estimates for graphs in warped product spaces. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 86, p. 21-pg., 2023-01-13. (21/09534-4, 18/03721-4, 18/23202-1)

BARRETO, ALEXANDRE PAIVA; FONTENELE, FRANCISCO; HARTMANN, LUIZ. On regular algebraic hypersurfaces with non-zero constant mean curvature in Euclidean spaces. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, v. N/A, p. 8-pg., 2021-09-06. (18/23202-1, 18/03721-4, 19/20854-0)

BARRETO, ALEXANDRE PAIVA; FONTENELE, FRANCISCO. On complete hypersurfaces with negative Ricci curvature in Euclidean spaces. REVISTA MATEMATICA IBEROAMERICANA, v. 39, n. 4, p. 6-pg., 2023-01-01. (19/20854-0, 18/03721-4)