Finsler interpolation inequalities

By Shin-ichi Ohta. 2009

280 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/db9657b1a3bdba1f2e661e3db78a1c7374a2b0d6

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In Applied Mathematics

In Astronomy and Astrophysics

Citations in the corpus

Heat Flow and Calculus on Metric Measure Spaces with Ricci Curvature Bounded Below—The Compact Case (2012, background): “This means that if we have a smooth compact Finsler manifold (that is: a differentiable manifold endowed with a norm— possibly not coming from an inner product—on each tangent space which varies smoothly on the base point) endowed with an arbitrary positive C∞ measure, then this space has Ricci curv”
Li–Yau and Harnack type inequalities in RCD∗(K,N) metric measure spaces (2013, background): “As a matter of facts, both the CD(K,N) and CD∗(K,N) conditions include Finsler geometries [31]-[39].”
Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds (2015, methodology): “geodesically complete and endowed with a C∞ probability measure min a such a way that the associated m.m.s. (X,F, ) satisﬁes the CD∗(K,N) condition. This class of spaces has been investigated by Ohta [54] who established the equivalence between the Curvature Dimension condition and a Finsler-version”
Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below (2011, background): “ below for metric measure spaces. It is well known that LSV spaces, while stable under Gromov-Hausdorﬀ convergence [39] and consistent with the smooth Riemannian case, include also Finsler geometries [31]. It is therefore natural to look for additional axioms, still stable and consistent, that rule ”
An optimal anisotropic Poincaré inequality for convex domains (2011, methodology): “Particularly, many problems related to the first eigenvalue of the anisotropic Laplacian have already been considered in [Belloni et al. 2003; Ge and Shen 2001; Kawohl 2011; Ohta 2009; Wang and Xia 2011a].”
Heat flow on Finsler manifolds (2008, methodology): “ipschitz continuous and twice diﬀerentiable a.e. (see [Oh3]). We say that ϕis d2/2-convex if −ϕis d2/2-concave. Then the Brenier-McCann characterization of optimal transport states the following (see [Oh4]): Theorem 6.2 For any µ∈Pac(M) and any ν ∈P(M), there exists a unique d2/2-convex function ϕ: ”
Uniform convexity and smoothness, and their applications in Finsler geometry (2009, background): “In fact, in a recent work of the author [23], Theorem 7.”