Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gradient estimates via two-point functions for elliptic equations on
  manifolds   We derive estimates relating the values of a solution at any two points to
the distance between the points, for quasilinear isotropic elliptic equations
on compact Riemannian manifolds, depending only on dimension and a lower bound
for the Ricci curvature. These estimates imply sharp gradient bounds relating
the gradient of an arbitrary solution at given height to that of a symmetric
solution on a warped product model space. We also discuss the problem on
Finsler manifolds with nonnegative weighted Ricci curvature, and on complete
manifolds with bounded geometry, including solutions on manifolds with boundary
with Dirichlet boundary condition. Particular cases of our results include
gradient estimates of Modica type.

32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th