Free Boundary Minimal Submanifolds in Euclidean Balls and Ricci Surfaces

• Grant number: 23/14796-3
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Effective date (Start): January 01, 2024
• Effective date (End): December 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Paolo Piccione
• Grantee: Roney Pereira dos Santos
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 22/16097-2 - Modern methods in differential geometry and geometric analysis, AP.TEM

Abstract

In this project, we intend to study how conformal changes influence the geometry of free boundary minimal surfaces in the Euclidean ball. In addition, we would also like to understand whether it is possible to conclude rigidity results in the conformal class of such surfaces.We also intend to study the geometry of a special type of Riemannian surfaces that admit minimal immersion in three-dimensional Euclidean space and whose Gaussian curvature satisfies a certain partial differential equation. These surfaces are known as Ricci surfaces.