Abstract
In this note we supply the detailed proof of the entropy asymptotics on manifolds with nonnegative Ricci curvature. We also discuss the possible connections between the large time behavior of the entropy and the existence of harmonic functions.
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References
V.A. Kaimanovich, Brownian motion and harmonic functions on covering manifolds. An entropy approach. Soviet Math. Dokl. 33 (1986), 812–816.
F. Ledrappier, Harmonic measures and Bowen-Margulis measures. Israel J. Math. 71 (1990), 275–287.
P. Li, L.-F. Tam and J. Wang, Sharp bounds for the Green’s function and the heat kernel, Math. Res. Lett. 4 (1997), no. 4, 589–602.
Munteanu, O., On a characterization of the complex hyperbolic space. ArXiv:0802.0307.
L. Ni, The entropy formula for linear heat equation, J. Geom. Anal. 14 (2004), 87–100.
L. Ni, Addenda to “The entropy formula for linear heat equation”, J. Geom. Anal. 14 (2004), 369–374.
L. Ni, A monotonicity formula on complete Kähler manifolds with nonnegative bisectional curvature, J. Amer. Math. Soc. 17 (2004), 909–946.
L. Ni, Ancient solutions to Kähler-Ricci flow. Math. Res. Lett. 12 (2005), no. 5–6, 633–653.
X.-D. Wang, Harmonic functions, entropy, and a characterization of the hyperbolic space, preprint.
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Ni, L. (2010). The Large Time Asymptotics of the Entropy. In: Complex Analysis. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0009-5_18
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DOI: https://doi.org/10.1007/978-3-0346-0009-5_18
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0346-0008-8
Online ISBN: 978-3-0346-0009-5
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