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pro vyhledávání: '"Volume entropy"'
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
Autor:
Garcia-Lara, Rene
We study a family of metrics on Euclidean space that generalize the left-invariant metric of the SOL group and the metric of the logarithmic model of Hyperbolic space. Suppose G is a connected, simply-connected, Heintze group of Abelian type with dia
Externí odkaz:
http://arxiv.org/abs/2410.10631
Autor:
Li, Mingxiang
This is a continuation of our previous work (Advances in Mathematics 450 (2024), Paper No. 109768). In this paper, we characterize complete metrics with finite total Q-curvature as normal metrics for all dimensional cases. Secondly, we introduce anot
Externí odkaz:
http://arxiv.org/abs/2408.03640
Autor:
Satoh, Hiroyasu
Harmonic manifolds of hypergeometric type form a class of non-compact harmonic manifolds that includes rank one symmetric spaces of non-compact type and Damek-Ricci spaces. When normalizing the metric of a harmonic manifold of hypergeometric type to
Externí odkaz:
http://arxiv.org/abs/2405.05896
Autor:
Mazzoli, Filippo, Viaggi, Gabriele
We investigate properties of the pseudo-Riemannian volume, entropy, and diameter for convex cocompact representations $\rho : \Gamma \to \mathrm{SO}(p,q+1)$ of closed $p$-manifold groups. In particular: We provide a uniform lower bound of the product
Externí odkaz:
http://arxiv.org/abs/2312.17137
We show that any closed hyperbolic 3-manifold M admits a Riemannian metric with scalar curvature at least -6, but with volume entropy strictly larger than 2. In particular, this construction gives counterexamples to a conjecture of I. Agol, P. Storm
Externí odkaz:
http://arxiv.org/abs/2312.00138
Autor:
Li, Mingxiang
In this paper, we investigate a conformally flat and complete manifold $(M,g)=(\mathbb{R}^n,e^{2u}|dx|^2)$ with finite total Q-curvature. We introduce a new volume entropy, incorporating the background Euclidean metric, and demonstrate that the metri
Externí odkaz:
http://arxiv.org/abs/2306.15623
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Autor:
Chen, Lina, Xu, Shicheng
The volume entropy of a compact metric measure space is known to be the exponential growth rate of the measure lifted to its universal cover at infinity. For a compact Riemannian $n$-manifold with a negative lower Ricci curvature bound and a upper di
Externí odkaz:
http://arxiv.org/abs/2211.01082
Akademický článek
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