Yau's gradient estimates on Alexandrov spaces

By Hui-Chun Zhang, Xiping Zhu. 2010

59 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/1530f4c713a2a4594709de05662b67c351c03f6f

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In Applied Mathematics

In Astronomy and Astrophysics

Citations in the corpus

On the equivalence of the entropic curvature-dimension condition and Bochner’s inequality on metric measure spaces (2013, background): “Ohta & Sturm [32] proved it for Finsler spaces and Gigli, Kuwada & Ohta [21] and Zhang & Zhu [43] for Alexandrov spaces.”
Heat Flow on Alexandrov Spaces (2010, background): “They even proceeded their study to [45, 35], where they showed a Bochner type formula and Li-Yau estimates under their own notion of lower Ricci curvature bound which is stronger than the one of Lott-Sturm-Villani.”
Gradient estimates for heat kernels and harmonic functions (2017, methodology): “In recent years, in a series of works [13, 52, 72, 73, 114, 115], Yau’s gradient estimate for harmonic functions and Li-Yau’s gradient estimate for heat kernels (and their local versions) have been further generalised to metric measure spaces and graphs satisfying suitable curvature assumptions; we ”
Ricci curvature and $L^p$-convergence (2012, result): “ense subspace in L2(B R(m∞)) and that this is stronger than Γ2-condition. See Remarks 4.21 and 4.28. It is worth pointing out that recently Zhang-Zhu proved a similar result on an Alexandrov space in [61]. On the other hand in [31] the author deﬁned the (geometric) Laplacian ∆gM∞ f for a weakly twic”
Cheeger-harmonic functions in metric measure spaces revisited (2013, background): “Notice that Zhang and Zhu [35] have proved Yau’s gradient est imate on Alexandrov spaces with a new Ricci curvature condition (see [34]).”