논문KCI 등재
Li-Yau gradient estimates on closed manifolds under Bakry-\'Emery Ricci curvature conditions
대한수학회 (The Korean Mathematical Society)|2023.09|대한수학회지 (Journal of the KMS)|제60권 제5호|pp. 1023-1041|DOI 10.4134/JKMS.j220589
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초록
In this paper, motivated by the work of Q.~S.~Zhang in \cite{ZQ}, we derive optimal Li-Yau gradient bounds for positive solutions of the $f$-heat equation on closed manifolds with Bakry-\'Emery Ricci curvature bounded below.
Abstract
In this paper, motivated by the work of Q.~S.~Zhang in \cite{ZQ}, we derive optimal Li-Yau gradient bounds for positive solutions of the $f$-heat equation on closed manifolds with Bakry-\'Emery Ricci curvature bounded below.
참고문헌 (28)
- 84, "Seminaire de probabilit´es XIX 1983", pp.1985, D. Bakry
- D. Bakry, "Harnack inequalities on a manifold with positive or negative Ricci curvature", Rev. Mat. Iberoam, 15(1), pp.143~179 (1999)[DOI]
- R. H. Bamler, "Convergence of Ricci flows with bounded scalar curvature", Ann. of Math, 188(3), pp.753~831 (2018)[DOI]
- N. Charalambous, "Elliptic and parabolic equations", pp.45~61 (2015), Springer
- X. Chen, "Space of Ricci flows (II)—Part B: Weak compactness of the flows", J. Differential Geom, 116(1), pp.1~123 (2020)[DOI]
- B. Chow, "Hamilton’s Ricci Flow", Graduate Studies in Mathematics, 77 (2006), Amer. Math. Soc[DOI]
- "Comparison geometry for Ricci curvature"[URL]
- N. Garofalo, "Li-Yau and Harnack type inequalities in RCD∗(K,N)metric measure spaces", Nonlinear Anal, 95, pp.721~734 (2014)[DOI]
- R. S. Hamilton, "A matrix Harnack estimate for the heat equation", Comm. Anal. Geom, 1(1), pp.113~126 (1993)[DOI]
- Y. Li, "Li-Yau-Hamilton estimates and Bakry-Emery-Ricci curvature", Nonlinear Anal, 113, pp.1~32 (2015)[DOI]
- J. Li, "Differential Harnack inequalities on Riemannian manifolds I : linear heat equation", Adv. Math, 226(5), pp.4456~4491 (2011)[DOI]
- P. Li, "On the parabolic kernel of the Schr¨odinger operator", Acta Math, 156(3-4), pp.153~201 (1986)[DOI]
- J. Lott, "Some geometric properties of the Bakry-´ Emery-Ricci tensor", Comment. Math. Helv, 78(4), pp.865~883 (2003)[DOI]
- G. Perelman, "The entropy formula for the Ricci flow and its geometric applications", ~
- B. Qian, "Remarks on differential Harnack inequalities", J. Math. Anal. Appl, 409(1), pp.556~566 (2014)[DOI]
- Z. M. Qian, "Sharp spectral gap and Li-Yau’s estimate on Alexandrov spaces", Math. Z, 273(3-4), pp.1175~1195 (2013)[DOI]
- G. Tian, "Regularity of K¨ahler-Ricci flows on Fano manifolds", Acta Math, 216(1), pp.127~176 (2016)[DOI]
- F. Y. Wang, "Gradient and Harnack inequalities on noncompact manifolds with boundary", Pacific J. Math, 245(1), pp.185~200 (2010)[DOI]
- G. Wei, "Comparison geometry for the Bakry-Emery Ricci tensor", J. Differential Geom, 83(2), pp.377~405 (2009)[DOI]
- J. Y. Wu, "Heat kernel on smooth metric measure spaces and applications", Math. Ann, 365(1-2), pp.309~344 (2016)[DOI]
- S. -T. Yau, "Harnack inequality for non-self-adjoint evolution equations", Math. Res. Lett, 2(4), pp.387~399 (1995)[DOI]
- C. Yu, "Sharp Li-Yau-type gradient estimates on hyperbolic spaces", J. Geom. Anal, 30(1), pp.54~68 (2020)[DOI]
- C. Yu, "Recurrence relations for heat kernels on spheres", J. Math. Anal. Appl, 507(2), pp.14~ (2022)[DOI]
- C. Yu, "Li-Yau multiplier set and optimal Li-Yau gradient estimate on hyperbolic spaces", Potential Anal, 56(2), pp.191~211 (2022)[DOI]
- Q. S. Zhang, "A Sharp Li-Yau gradient bound on Compact Manifolds", ~
- H.-C. Zhang, "Local Li-Yau’s estimates on RCD∗(K,N) metric measure spaces", Calc. Var. Partial Differential Equations, 55(4), pp.30~ (2016)[DOI]
- Q. S. Zhang, "Li-Yau gradient bound for collapsing manifolds under integral curvature condition", Proc. Amer. Math. Soc, 145(7), pp.3117~3126 (2017)[DOI]
- Q. S. Zhang, "Li-Yau gradient bounds on compact manifolds under nearly optimal curvature conditions", J. Funct. Anal, 275(2), pp.478~515 (2018)[DOI]
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