ProjectGeometrie und Analysis unter verallgemeinerten Krümmungsbegriffen
Basic data
Title:
Geometrie und Analysis unter verallgemeinerten Krümmungsbegriffen
Duration:
01/09/2017 to 31/08/2019
Abstract / short description:
The main purpose of this proposal is twofold. In the first part we try to go beyond the current framework of weighted Ricci curvature on manifold: Besides trying to extend the non-smooth techniques in the presence of boundaries, the project tries to understand the Bakry-\'Emery Ricci tensor for $1$-forms and for non-conventional dimensions. The second part tries to understand isopermetry: Using the behavior at infinity in form of asymptotic flatness and local behavior in terms of scalar curvature, we hope to get strong local-to-global implications on the asymptotic volume growth. Another approach treats isoperimetric comparison principles in a purely synthetic way. Adding necessary conditions that allow a first order analysis, we hope to understand geometric and analytic implications that follow directly from the isoperimetric conditions.
Keywords:
geometry
Geometrie
analysis
Analysis
Krümmung (curvature)
Involved staff
Managers
Department of Mathematics
Faculty of Science
Faculty of Science
Local organizational units
Department of Mathematics
Faculty of Science
University of Tübingen
University of Tübingen
Funders
Bonn, Nordrhein-Westfalen, Germany