摘要

In Cabre (1997) [2], Cabre established an Alexandroff-Bakelman-Pucci (ABP) estimate on Riemannian manifolds with non-negative sectional curvatures and applied it to establish the Krylov-Safonov Harnack inequality on manifolds with non-negative sectional curvatures. In the present paper, we generalize the results of [2]. We obtain an ABP estimate on manifolds with Ricci curvatures bounded from below and apply this estimate to prove the Krylov-Safonov Harnack inequality on manifolds with sectional curvatures bounded from below. We also use this ABP estimate to study Minkowski-type inequalities. Published by Elsevier Inc.

  • 出版日期2013-1-15