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Article overview
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Measure Estimates, Harnack Inequalities and Ricci Lower Bound | | Yu Wang
; Xiangwen Zhang
; | | Date: |
28 Feb 2011 | | Abstract: | On a Riemannian metric-measure space, we establish an
Alexandrov-Bakelman-Pucci type measure estimate connecting Bakry-’Emery Ricci
curvature lower bound, modified Laplacian and the measure of certain special
sets. We apply this estimate to prove Harnack inequalities for the modified
Laplacian operator and fully non-linear operators. These inequalities seem not
available in the literature; And our proof, solely based on the ABP estimate,
does not involve any Sobolev inequalities nor gradient estimate. We also
propose a question regarding the characterization of Ricci lower bound by the
Harnack inequality. | | Source: | arXiv, 1102.5567 | | Services: | Forum | Review | PDF | Favorites | |
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