Volumes in normed vector spaces and Finsler manifolds

• Applicant: Professor Dr. Andreas Bernig
• Subject Area: Mathematics
• Term: from 2014 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 260592914

Convexity properties of volumes in normed spaces and Finsler manifolds are related to fundamental problems in convexity, geometric inequalities and geometric analysis. In this project, convexity of different notions of volumes, like Busemann volume, Holmes-Thompson volume, and the recently introduced volume based on centroid bodies will be studied. Moreover, consequences of convexity for lengths of closed geodesics on Finsler manifolds, minimal and extremal submanifolds and geometric inequalities like the conjectured Petty's projection inequality will be investigated.

• DFG Programme: Research Grants