Nearby in the stack

Lipschitz-Volume Rigidity and Globalization · arXivDesk

1911.00120Oct 31, 2019

Lipschitz-Volume Rigidity and Globalization

Nan Li

Differential Geometry Metric Geometry

Abstract

Let $X$ and $Y$ be length metric spaces. Let $\mathcal H^n$ denote the $n$ -dimensional Hausdorff measure. The Lipschitz-Volume Rigidity is a property that if there exists a 1-Lipschitz map $f\colon X\to Y$

Briefing

What this paper is actually doing

Sign in and connect a model key to generate a briefing for this paper.

Claims

Methods

Limitations

Socratic margin

Ask the abstract

Questions are grounded in the title and abstract. If the PDF is required, arXivDesk will say so.

Sign in to ask questions about this paper.

Nearby in the stack

and

0<\mathcal H^n(X)=\mathcal H^n(f(X))<\infty

, then

f

preserves the length of path. This property holds for smooth manifolds but doesn't hold for all singular spaces. We survey the Lipschitz-Volume Rigidity Theorems on singular spaces with lower curvature bounds and discuss some related open problems.

2501.05974

over 1 year ago

The Lipschitz-volume rigidity problem for metric manifolds

Denis Marti

Differential Geometry Metric Geometry

2209.12545

almost 4 years ago

Filling minimality and Lipschitz-volume rigidity of convex bodies among integral current spaces

Giuliano Basso, Paul Creutz, Elefterios Soultanis

Differential Geometry Functional Analysis Metric Geometry

1310.8373

almost 13 years ago

Lipschitz-Volume rigidity on limit spaces with Ricci curvature bounded from below

Nan Li, Feng Wang

Differential Geometry

1110.5498

almost 15 years ago

Lipschitz-Volume rigidity in Alexandrov geometry

Nan Li

Differential Geometry Metric Geometry

1212.6685

over 13 years ago

Generic Global Rigidity in Complex and Pseudo-Euclidean Spaces

Steven J. Gortler, Dylan P. Thurston

Metric Geometry

2608.13553

3 days ago

Heat kernel geometry and Gromov's volume growth conjecture

Jian Ge

Differential Geometry