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- Title
MEASURE ESTIMATES, HARNACK INEQUALITIES AND RICCI LOWER BOUND.
- Authors
Yu Wang; Xiangwen Zhang
- Abstract
On the Riemannian metric-measure space, we establish an Ale-xandrov-Bakelman-Pucci type estimate connecting the Bakry-Emery Ricci curvature lower bound, the modified Laplacian and the measure of certain special sets. We apply this estimate to prove the Harnack inequalities for the modified Laplacian operator (and fully non-linear operators, see the Appendix). These inequalities seem not available in the literature and our proof, based solely on the ABP estimate, does not use standard techniques.
- Subjects
RIEMANNIAN metric; LAPLACIAN operator; PROOF theory; MATHEMATICAL models; MATHEMATICAL analysis
- Publication
Universitatis Iagellonicae Acta Mathematica, 2018, Vol 55, p21
- ISSN
0083-4386
- Publication type
Article
- DOI
10.4467/20843828AM.18.002.9718