Abstract
We consider second-order linear elliptic operators of nondivergence type which are intrinsically defined on Riemannian manifolds. Cabré proved a global Krylov-Safonov Harnack inequality under the assumption that the sectional curvature is nonnegative. We improve Cabré's result and, as a consequence, we give another proof to the Harnack inequality of Yau for positive harmonic functions on Riemannian manifolds with nonnegative Ricci curvature using the nondivergence structure of the Laplace operator.
Original language | English |
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Pages (from-to) | 281-293 |
Number of pages | 13 |
Journal | Pacific Journal of Mathematics |
Volume | 213 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2004 Feb |
All Science Journal Classification (ASJC) codes
- Mathematics(all)