Levi-flat CR structures and comparison principles

• Grant number: 23/17607-7
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2024
• End date: February 28, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Paulo Leandro Dattori da Silva
• Grantee: Vinícius Novelli da Silva
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 24/12753-8 - Geometric theory of PDE and multidimensional complex analysis, AP.TEM

Abstract

This research project deals with a correspondence between Levi-flat CR structures and systems of real vector fields. In several different models, this correspondence allows to obtain results about vanishing of cohomology spaces, global solvability and global hypoellipticity of one of the structures from information about the other. In presence of a Lie group action, the naturally associated real models of such CR structures have been heavily studied recently.