Zobrazeno 1 - 10
of 2 012
pro vyhledávání: '"53c23"'
Autor:
Fiacchi, Matteo, Nikolov, Nikolai
We provide sharp estimates for the intrinsic distances of Finsler metrics with precise boundary estimates. These metrics include the Kobayashi-Hilbert metric near strongly convex points, the minimal metric near convex and strongly minimally convex po
Externí odkaz:
http://arxiv.org/abs/2412.10012
Autor:
Murugan, Mathav
Given a strongly local Dirichlet form on a metric measure space that satisfies Gaussian heat kernel bounds, we show that the martingale dimension of the associated diffusion process coincides with Cheeger's analytic dimension of the underlying metric
Externí odkaz:
http://arxiv.org/abs/2412.06737
The goal of this paper is to provide an expository description of a result of Carrasco Piaggio connecting the Ahlfors regular conformal dimension of a compact uniformly perfect doubling metric space with the combinatorial $p$-moduli of the metric spa
Externí odkaz:
http://arxiv.org/abs/2412.05549
We discuss $(K,N)$-convexity and gradient flows for $(K,N)$-convex functionals on metric spaces, in the case of real $K$ and negative $N$. In this generality, it is necessary to consider functionals unbounded from below and/or above, possibly attaini
Externí odkaz:
http://arxiv.org/abs/2412.04574
We study the Wasserstein barycenter problem in the setting of non-compact, non-smooth extended metric measure spaces. We introduce a couple of new concepts and obtain the existence, uniqueness, absolute continuity of the Wasserstein barycenter, and p
Externí odkaz:
http://arxiv.org/abs/2412.01190
Autor:
Zhu, Zhifei
In this article, we prove a generalization of our previous result in [12]. In particular, we show that for an $n$-dimensional, simply connected Riemannian manifold with diameter $D$ and volume $V$. Suppose that $M$ admits a good cover consisting of $
Externí odkaz:
http://arxiv.org/abs/2412.01161
Autor:
Lytchak, Alexander, Wilking, Burkhard
We prove that a Riemannian submersion between smooth, compact, non-negatively curved Riemannian manifolds has to be smooth, resolving a conjecture by Berestovskii--Guijarro. We show that without any curvature assumption, the smoothness of the base is
Externí odkaz:
http://arxiv.org/abs/2411.15324
Autor:
Hebda, James J., Katz, Mikhail G.
We study the maximum ratio of the Euclidean norm to the comass norm of p-covectors in Euclidean n-space and improve the known upper bound found in the standard references by Whitney and Federer. We go on to prove stable systolic inequalities when the
Externí odkaz:
http://arxiv.org/abs/2411.13966
Autor:
Toyoda, Tetsu
We establish a family of inequalities that hold true on any $6$ points in any $\mathrm{CAT}(0)$ space. We prove that the validity of these inequalities does not follow from any properties of $5$-point subsets of $\mathrm{CAT}(0)$ spaces. In particula
Externí odkaz:
http://arxiv.org/abs/2411.13877
Autor:
Connell, Chris, Dai, Xianzhe, Núñez-Zimbrón, Jesús, Perales, Raquel, Suárez-Serrato, Pablo, Wei, Guofang
We develop the barycenter technique of Besson--Courtois--Gallot so that it can be applied on RCD metric measure spaces. Given a continuous map $f$ from a non-collapsed RCD$(-(N-1),N)$ space $X$ without boundary to a locally symmetric $N$-manifold we
Externí odkaz:
http://arxiv.org/abs/2411.04327