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Nonminimal coupling, quantum scalar field stress-energy tensor and energy conditions on global anti-de Sitter space-time. [PDF]

Gen Relativ Gravit
Namasivayam S, Winstanley E.
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Ollivier Persistent Ricci Curvature-Based Machine Learning for the Protein–Ligand Binding Affinity Prediction

Journal of Chemical Information and Modeling, 2021
Efficient molecular featurization is one of the major issues for machine learning models in drug design. Here, we propose a persistent Ricci curvature (PRC), in particular, Ollivier PRC (OPRC), for the molecular featurization and feature engineering, for
JunJie Wee, Kelin Xia
exaly   +2 more sources

Rigidities of isoperimetric inequality under nonnegative Ricci curvature

Journal of the European Mathematical Society (Print), 2022
The sharp isoperimetric inequality for non-compact Riemannian manifolds with nonnegative Ricci curvature and Euclidean volume growth has been obtained in increasing generality with different approaches in a number of contributions culminated by Balogh ...
Fabio Cavalletti, D. Manini
semanticscholar   +1 more source

Positive Intermediate Ricci Curvature on Fibre Bundles

Symmetry, Integrability and Geometry: Methods and Applications, 2022
We prove a canonical variation-type result for submersion metrics with positive intermediate Ricci curvatures. This can then be used in conjunction with surgery techniques to establish the existence of metrics with positive intermediate Ricci curvatures ...
Philipp Reiser, D. Wraith
semanticscholar   +1 more source

Complete Logarithmic Sobolev inequality via Ricci curvature bounded below II

Journal of Topology and Analysis (JTA), 2021
We study the “geometric Ricci curvature lower bound”, introduced previously by Junge, Li and LaRacuente, for a variety of examples including group von Neumann algebras, free orthogonal quantum groups [Formula: see text], [Formula: see text]-deformed ...
Michael Brannan, Li Gao, M. Junge
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Sharp isoperimetric and Sobolev inequalities in spaces with nonnegative Ricci curvature

Mathematische Annalen, 2020
By using optimal mass transport theory we prove a sharp isoperimetric inequality in $${\textsf {CD}} (0,N)$$ CD ( 0 , N ) metric measure spaces assuming an asymptotic volume growth at infinity.
Z. Balogh, Alexandru Krist'aly
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Weighted Ricci Curvature

Springer Monographs in Mathematics, 2021
In Part I, we saw that the natural notions of Finsler curvatures (the flag and Ricci curvatures) can be introduced through the behavior of geodesics, and then several comparison theorems follow smoothly by similar arguments to the Riemannian case, or through the characterizations of these curvatures from the Riemannian geometric point of view.
Shin-ichi Ohta
semanticscholar   +3 more sources

Riemann Curvature and Ricci Curvature [PDF]

, 2012
Curvatures are the central concept in geometry. The notion of curvature introduced by B. Riemann faithfully reveals the local geometric properties of a Riemann metric. This curvature is called the Riemann curvature in Riemannian geometry. The Riemann curvature can be extended to Finsler metrics as well as the sectional curvature.
Xinyue Cheng, Zhongmin Shen
openaire   +1 more source

Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature

Inventiones Mathematicae, 2018
In this paper we consider complete noncompact Riemannian manifolds (M, g) with nonnegative Ricci curvature and Euclidean volume growth, of dimension n≥3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts ...
Virginia Agostiniani, Mattia Fogagnolo, L. Mazzieri   +2 more
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