Rigidity of the 1-Bakry–Émery Inequality and Sets of Finite Perimeter in RCD Spaces

By Ambrosio Luigi, Brue Elia, Semola Daniele. Geometric and Functional Analysis, 2018

60 citations recorded by the source corpus.

This note is dedicated to the study of the asymptotic behaviour of sets of finite perimeter over RCD(K,N) metric measure spaces. Our main result asserts existence of a Euclidean tangent half-space almost everywhere with respect to the perimeter measure and it can be improved to an existence and uniqueness statement when the ambient is non collapsed. As an intermediate tool, we provide a complete characterization of the class of RCD(0,N) spaces for which there exists a nontrivial function satisfying the equality in the 1-Bakry-\'Emery inequality. This result is of independent interest and it is new, up to our knowledge, even in the smooth framework.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/984ce70a437ef712283320ed8c1d9299f3900156

How researchers see this paper

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In Applied Mathematics

1. Enrico Pasqualetto
2. Elia Brué
3. Semola Daniele

In Astronomy and Astrophysics

1. Enrico Pasqualetto
2. Elia Brué
3. Semola Daniele

Citations in the corpus

• Rectifiability of the reduced boundary for sets of finite perimeter over $\RCD(K,N)$ spaces. (2019, methodology): “,n covers X up to a |DχE |-negligible set we need to use the following result that has been proven in the appendix of [2].”