On the entropies of hypersurfaces with bounded mean curvature

• Grant number: 25/10522-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2025
• End date: July 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Fernando Manfio
• Grantee: Gabriel Balbão Bazon
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This research project aims to study on the concept of entropy in hypersurfaces of a Riemannian manifold, comparing the entropy volume of the hypersurface with that of the environment, provided that certain geometric conditions are satisfied. As an application, we will study some recent contributions to the do Carmo's question about stable Euclidean hypersurfaces, with constant mean curvature. (AU)