Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New formulas for the Laplacian of distance functions and applications   The goal of the paper is to prove an exact representation formula for the
Laplacian of the distance (and more generally for an arbitrary 1-Lipschitz
function) in the framework of metric measure spaces satisfying Ricci curvature
lower bounds in a synthetic sense (more precisely in essentially non-branching
MCP(K,N)-spaces). Such a representation formula makes apparent the classical
upper bounds and also some new lower bounds, together with a precise
description of the singular part. The exact representation formula for the
Laplacian of 1-Lipschitz functions (in particular for distance functions) holds
also (and seems new) in a general complete Riemannian manifold. We apply these
results to prove the equivalence of CD(K,N) and a dimensional Bochner
inequality on signed distance functions. Moreover we obtain a measure-theoretic
Splitting Theorem for infinitesimally Hilbertian essentially non-branching
spaces verifying MCP(0,N).

5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph