Orthogonal geodesics in manifolds with singular boundary. Applications to the theory of minimal surfaces.

• Grant number: 22/13010-3
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: February 01, 2023
• End date: July 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Paolo Piccione
• Grantee: Paolo Piccione
• Visiting researcher: Dario Corona
• Visiting researcher institution: Università degli Studi di Camerino (UNICAM), Italy
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 16/23746-6 - Algebraic, topological and analytical techniques in differential geometry and geometric analysis, AP.TEM

Abstract

The main theme of the research proposed in this project will be the study of geodesics in Riemannian or Finslerian compact manifolds with singular boundary. In particular, together with Prof. Piccione, we will study the existence of geodesicsthat connect a point in the interior with a point on the boundary, in the case where the metric degenerates on the boundary with a conformal factor that vanishes, and with zero of order greater than or equal to two. We intend to apply the results to the study of minimal surfaces that are invariant by the action of a symmetric group, via the principle of Hsiang and Lawson. (AU)