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October 2012 An extension of Schäffer's dual girth conjecture to Grassmannians
Dmitry Faifman
J. Differential Geom. 92(2): 201-220 (October 2012). DOI: 10.4310/jdg/1352297806

Abstract

In this note we introduce a natural Finsler structure on convex surfaces, referred to as the quotient Finsler structure, which is dual in a sense to the inclusion of a convex surface in a normed space as a submanifold. It has an associated quotient girth, which is similar to the notion of girth defined by Schäffer. We prove the analogs of Schäffer’s dual girth conjecture (proved by Álvarez-Paiva) and the Holmes–Thompson dual volumes theorem in the quotient setting. We then show that the quotient Finsler structure admits a natural extension to higher Grassmannians, and prove the corresponding theorems in the general case. We follow Álvarez-Paiva’s approach to the problem, namely, we study the symplectic geometry of the associated co-ball bundles. For the higher Grassmannians, the theory of Hamiltonian actions is applied.

Citation

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Dmitry Faifman. "An extension of Schäffer's dual girth conjecture to Grassmannians." J. Differential Geom. 92 (2) 201 - 220, October 2012. https://doi.org/10.4310/jdg/1352297806

Information

Published: October 2012
First available in Project Euclid: 7 November 2012

zbMATH: 1264.53067
MathSciNet: MR2998671
Digital Object Identifier: 10.4310/jdg/1352297806

Rights: Copyright © 2012 Lehigh University

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Vol.92 • No. 2 • October 2012
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