ProjectGeometrie und Analysis unter verallgemeinerten Krümmungsbegriffen

Basic data

Title:
Geometrie und Analysis unter verallgemeinerten Krümmungsbegriffen
Duration:
9/1/2017 to 8/31/2019
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

Local organizational units

Department of Mathematics
Faculty of Science
University of Tübingen

Funders

Bonn, Nordrhein-Westfalen, Germany
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