Min-max minimal surfaces

• Grant number: 18/08511-8
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• Start date: October 03, 2018
• End date: March 02, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Alexandre Paiva Barreto
• Grantee: Anderson Felipe Viveiros
• Supervisor: Fernando Coda dos Santos Cavalcanti Marques
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Institution abroad: Princeton University, United States
• Associated to the scholarship: 17/05800-6 - Minimal surfaces and the Almgren-Pitts Min-Max theory, BP.MS

Abstract

We will study the Almgren-Pitts Min-Max method to construct and analyze minimal surfaces. Our research will be guided by the recent article Rigidity of min-max minimal spheres in three-manifolds, by F. C. Marques and A. Neves, where it is proved, among other results, that any metric on a three-sphere which has scalar curvature greater than or equal to 6 and is not round must have an embedded minimal sphere of area strictly smaller than 4pi and index at most one. (AU)