Volumes on Normed and Finsler Spaces
By J. '. Paiva, A. C. Thompson. 2004
136 citations recorded by the source corpus.
View Paper: https://www.semanticscholar.org/paper/380ecf30761cd130d93d4f18b8a58947a56efbd4
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- A. Lytchak
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- Shin-ichi Ohta
- G. Berck
- Guido De Philippis
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- Francesco Ghiraldin
Citations in the corpus
- Contact geometry and isosystolic inequalities (2011, background): “This is the Holmes-Thompson volume of a Finsler manifold (see [28] and [2] for a detailed discussion of this definition).”
- Intrinsic structure of minimal discs in metric spaces (2016, methodology): “Among such definitions of area the most important ones are the (Busemann)-Hausdorff area H2, the Holmes-Thompson area µht, the (Benson)-Gromov m∗-measure and (Ivanov’s) inscribed Riemannian area µi.”
- Finsler interpolation inequalities (2009, background): “Different from Riemannian manifolds, there is a variety of canonical measures on Finsler manifolds, such as the Busemann-Hausdorff measure, the Holmes-Thompson measure and so forth (see [AT]).”
- What is wrong with the Hausdorff measure in Finsler spaces (2004, methodology): “Its deep ties to convexity, differential geometry, and integral geometry (see [21], [5], and [1]) have made the Holmes-Thompson volume easier to study than the Hausdorff measure.”
- The Binet-Legendre Metric in Finsler Geometry (2011, unknown): “It is also known, but somewhat delicate to prove, that if F is a reversible Finsler metric on M , then dμF coincides with the n-dimensional Hausdorff measure of the metric space associated to the Finsler structure, see [2, 9, 11, 12].”
- Area Minimizing Discs in Metric Spaces (2015, background): “Recall from [4] the following definition.”
- Rectifiability of Varifolds with Locally Bounded First Variation with Respect to Anisotropic Surface Energies (2016, background): “In this respect, let us recall that the study of convexity notions for integrands defined on the d-dimensional Grassmannian is an active field of research, where several basic questions are still open, see [7, 6] and the survey [4].”