Dual mixed volumes and isosystolic inequalities
Juan Carlos Alvarez Paiva
TL;DR
This paper extends dual mixed volume theory to cotangent bundles and applies it to establish isosystolic inequalities for Hamiltonian systems and Finsler metrics, advancing geometric analysis in these areas.
Contribution
It introduces an extension of dual mixed volumes to cotangent bundles and derives new isosystolic inequalities for Hamiltonian and Finsler geometries.
Findings
Established new isosystolic inequalities for Hamiltonian systems.
Extended dual mixed volume theory to cotangent bundles.
Provided geometric bounds for Finsler metrics.
Abstract
The theory of dual mixed volumes is extended to star bodies in cotangent bundles and is used to prove several isosystolic inequalities for Hamiltonian systems and Finsler metrics.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Geometric Analysis and Curvature Flows · Point processes and geometric inequalities