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PDF(449 KB)
PDF(449 KB)
图上曲率维数不等式的若干等价性质
Equivalent Properties of CD Inequalities on Graphs
本文研究局部有限图上的曲率维数不等式CD （n，K）的若干等价性质，包括梯度估计、Poincaré不等式和逆Poincaré不等式.还得到了局部有限图上的修正曲率维数不等式CDE'（∞，K）的其中一个等价性质，即梯度估计.
We study some equivalent properties of the curvature dimension inequality CD(n,K) on locally finite graphs. These equivalences are gradient estimate, Poincaré type inequalities and reverse Poincaré inequalities. We also obtain one equivalent property of gradient estimate for a new notion of curvature dimension inequality CDE (∞,K) at the same assumption on graphs.
热核 / 半群 / 曲率维数不等式 {{custom_keyword}} /
heat kernel / semigroup / curvature dimension inequality {{custom_keyword}} /
[1] Bakry D., Ledoux M., A logarithmic Sobolev form of the Li-Yau parabolic inequality, Rev. Mate. Iber., 2007, 22(2):683-702.
[2] Bakry D., Emery M., Diffusions Hypercontractives, Lecture Notes in Math., Springer, Berlin, 1985.
[3] Bauer F., Horn P., Lin Y., et al., Li-Yau inequality on graphs, J. Diff. Geom., 2015, 99(3):359-405.
[4] Chung F., Spectral Graph Theory, CBMS Regional Conference Series in Mathematics No. 92, Providence, 1997.
[5] Hua B. B., Lin Y., Stochastic completeness for graphs with curvature dimension conditions, Adv. Math., 2017, 306:279-302.
[6] Horn P., Lin Y., Liu Sh., et al., Volume doubling, Poincaré inequality and Guassian heat kernel estimate for nonnegative curvature graphs, arXiv:1411.5087.
[7] Keller M., Lenz D., Unbounded laplacians on graphs:basic spectral properties and the heat equation, Math. Mod. Nat. Phe., 2011, 5(4):198-224.
[8] Li P., Yau S. T., On the parabolic kernel of the Schrodinger operator, Acta Math., 1986, 156:153-201.
[9] Liu S. P., Münch F., Peyerimhoff N., Bakry-Emery curvature and diameter bounds on graphs, arXiv:1608.07778.
[10] Lin Y., Yau S. T., Ricci curvature and eigenvalue estimate on locally finite graphs, Math. Res. Let., 2010, 17(2):343-356.
[11] Liu S. P., Peyerimhoff N., Eigenvalue ratios of nonnegatively curved graphs, arXiv:1406.6617.
[12] Wang F. Y., Equivalent semigroup properties for curvature-dimension condition, Bull. Des Sci. Math., 2011, 135(6/7):803-815.
[13] Weber A., Analysis of the physical Laplacian and the heat flow on a locally finite graph, J. Math. Anal. Appl., 2012, 370(1):146-158.
国家自然科学基金资助项目（11671401）
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