Gigli N, Kuwada K, Ohta S, et al. Heat flow on Alexandrov spaces[J]. Communications on Pure and Applied Mathematics, 2010, 66(3): 307-331.
2
Erbar M, Kuwada K, Sturm K, et al. On the Equivalence of the Entropic Curvature-Dimension Condition and Bochner\u0027s Inequality on Metric Measure Spaces[J]. Inventiones Mathematicae, 2013, 201(3): 993-1071.
3
Z Qian · Huichun Zhang · Xiping Zhu. Sharp Spectral Gap and Li-Yau's Estimate on Alexandrov Spaces. 2011.
4
Ketterer C. Cones over metric measure spaces and the maximal diameter theorem[J]. Journal de Mathématiques Pures et Appliquées, 2013, 103(5): 1228-1275.
5
Jiang R. Cheeger-harmonic functions in metric measure spaces revisited[J]. Journal of Functional Analysis, 2013, 266(3): 1373-1394.
6
Xia C. Local gradient estimate for harmonic functions on Finsler manifolds[J]. Calculus of Variations and Partial Differential Equations, 2013: 849-865.
7
Jiang R, Koskela P. Isoperimetric inequality from the poisson equation via curvature[J]. Communications on Pure and Applied Mathematics, 2012, 65(8): 1145-1168.
8
Jiang R, Zhang H. Hamilton\u0027s Gradient Estimates and A Monotonicity Formula for Heat Flows on Metric Measure Spaces[J]. Nonlinear Analysis-theory Methods \u0026 Applications, 2015: 32-47.
9
Hua B, Xia C. A note on local gradient estimate on Alexandrov spaces[J]. Tohoku Mathematical Journal, 2013, 66(2): 259-267.
10
J X Huang · Huichun Zhang. Harmonic Maps Between Alexandrov Spaces. 2016.
In this paper, we establish a Bochner-type formula on Alexandrov spaces with Ricci curvature bounded below. Yau’s gradient estimate for harmonic functions is also obtained on Alexandrov spaces.