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We prove Gaussian type bounds for the fundamental solution of the conjugate heat equation evolving under the Ricci flow.
L p L^{p} and mean value properties of subharmonic functions on Riemannian manifolds
Peter Li and Richard Schoen · 1984
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On the parabolic kernel of the Schrödinger operator
Peter Li and Shing Tung Yau · 1986
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Heat kernels and spectral theory
E. B. Davies · 1990
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Uniformly elliptic operators on Riemannian manifolds
Laurent Saloff-Coste · 1992
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Ricci solitons on compact three-manifolds
Thomas Ivey · 1993
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A compactness property for solutions of the Ricci flow
Richard S. Hamilton · 1995
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The formation of singularities in the Ricci flow
Richard S. Hamilton · 1995
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Gaussian upper bounds for the heat kernel on arbitrary manifolds
Alexander Grigor ′ · 1997
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The fundamental solution on manifolds with time-dependent metrics
Christine M. Guenther · 2002
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Grisha Perelman · 2002
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Grisha Perelman · 2003
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Lei Ni · 2004
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Lei Ni · 2006
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Some gradient estimates for the heat equation on domains and for an equation by Perelman
Qi S. Zhang · 2006
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The Ricci flow: techniques and applications. Part I
Bennett Chow, Sun-Chin Chu, David Glickenstein, Christine Guenther, James Isenberg, Tom Ivey, Dan Knopf, Peng Lu, Feng Luo, and Lei Ni · 2007
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Ricci flow and the Poincaré conjecture
John Morgan and Gang Tian · 2007
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Noncompact shrinking 4-solitons with nonnegative curvature
Aaron Naber · 2007
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Differential Harnack estimates for backward heat equations with potentials under the Ricci flow
Xiaodong Cao · 2008
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Sobolev inequalities for manifolds evolving by Ricci flow
Shu-Yu Hsu · 2008
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A gradient estimate for all positive solutions of the conjugate heat equation under Ricci flow
Shilong Kuang and Qi S. Zhang · 2008
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Differential Harnack estimates for time-dependent heat equations with potentials
Xiaodong Cao and Richard S. Hamilton · 2009
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Strong uniqueness of the Ricci flow
Bing-Long Chen · 2009
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Gradient estimates for solutions of the heat equation under Ricci flow
Shiping Liu · 2009
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The logarithmic sobolev inequality along the ricci flow, 2007
Rugang Ye · 2007
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Qi S. Zhang · 2007
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A uniform Sobolev inequality under Ricci flow
Qi S. Zhang · 2007
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Marc Arnaudon, Kolehe Abdoulaye Coulibaly, and Anton Thalmaier · 2008
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The Ricci flow: techniques and applications. Part III
Bennett Chow, Sun-Chin Chu, David Glickenstein, Christine Guenther, James Isenberg, Tom Ivey, Dan Knopf, Peng Lu, Feng Luo, and Lei Ni
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Gradient estimates for the heat equation under the Ricci flow
Mihai Bailesteanua, Xiaodong Cao, and Artem Pulemotov · 2010
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On Type I Singularities in Ricci flow
Joerg Enders, Reto Müller, and Peter M. Topping · 2010
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Remarks on curvature behavior at the first singular time of the Ricci flow
Nam Q. Le and Natasa Sesum · 2010
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Sobolev inequalities, heat kernels under Ricci flow and the Poincaré conjecture
Qi S. Zhang · 2010
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