Displaying similar documents to “A rough curvature-dimension condition for metric measure spaces”

Angles between Curves in Metric Measure Spaces

Bang-Xian Han, Andrea Mondino (2017)

Analysis and Geometry in Metric Spaces

Similarity:

The goal of the paper is to study the angle between two curves in the framework of metric (and metric measure) spaces. More precisely, we give a new notion of angle between two curves in a metric space. Such a notion has a natural interplay with optimal transportation and is particularly well suited for metric measure spaces satisfying the curvature-dimension condition. Indeed one of the main results is the validity of the cosine formula on RCD*(K, N) metric measure spaces. As a consequence,...

Characterization of Low Dimensional RCD*(K, N) Spaces

Yu Kitabeppu, Sajjad Lakzian (2016)

Analysis and Geometry in Metric Spaces

Similarity:

In this paper,we give the characterization of metric measure spaces that satisfy synthetic lower Riemannian Ricci curvature bounds (so called RCD*(K, N) spaces) with non-empty one dimensional regular sets. In particular, we prove that the class of Ricci limit spaces with Ric ≥ K and Hausdorff dimension N and the class of RCD*(K, N) spaces coincide for N < 2 (They can be either complete intervals or circles). We will also prove a Bishop-Gromov type inequality (that is ,roughly speaking,...

On some type of curvature conditions

Mohamed Belkhelfa, Ryszard Deszcz, Małgorzata Głogowska, Marian Hotloś, Dorota Kowalczyk, Leopold Verstraelen (2002)

Banach Center Publications

Similarity:

In this paper we present a review of recent results on semi-Riemannian manifolds satisfying curvature conditions of pseudosymmetry type.

Curvature bounds for neighborhoods of self-similar sets

Steffen Winter (2011)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In some recent work, fractal curvatures C k f ( F ) and fractal curvature measures C k f ( F , · ) , k = 0 , ... , d , have been determined for all self-similar sets F in ℝ d , for which the parallel neighborhoods satisfy a certain regularity condition and a certain rather technical curvature bound. The regularity condition is conjectured to be always satisfied, while the curvature bound has recently been shown to fail in some concrete examples. As a step towards a better understanding of its meaning, we discuss several equivalent...