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Renormalization Group and the Ricci Flow [PDF]
Milan Journal of Mathematics, 2010 30 pages, 16 PNG figures, Conference talk at the Riemann International School of Mathematics: Advances in Number Theory and Geometry, Verbania April 19-24, 2009- Proceedings to appear in Milan Journal of Mathematics (Birkhauser)
Mauro Carfora
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University Lecture Series, 2020
This book gives an introduction to fundamental aspects of generalized Riemannian, complex, and K\"ahler geometry. This leads to an extension of the classical Einstein-Hilbert action, which yields natural extensions of Einstein and Calabi-Yau structures ...
M. Garcia‐Fernandez, J. Streets
semanticscholar +1 more source
This book gives an introduction to fundamental aspects of generalized Riemannian, complex, and K\"ahler geometry. This leads to an extension of the classical Einstein-Hilbert action, which yields natural extensions of Einstein and Calabi-Yau structures ...
M. Garcia‐Fernandez, J. Streets
semanticscholar +1 more source
A Note on Kähler–Ricci Flow on Fano Threefolds
Peking Mathematical Journal, 2022In this note, we show that the solution of Kähler–Ricci flow on every Fano threefold from Family No. 2.23 in the Mori–Mukai’s list develops type II singularity. In fact, we show that no Fano threefold from Family No.
Minghao Miao, G. Tian
semanticscholar +1 more source
International Journal of Mathematics, 2010
In this paper, we introduce the Sasaki–Ricci flow to study the existence of η-Einstein metrics. In the positive case any η-Einstein metric can be homothetically transformed to a Sasaki–Einstein metric. Hence it is an odd-dimensional counterpart of the Kähler–Ricci flow. We prove its well-posedness and long-time existence.
Smoczyk, Knut +2 more
openaire +3 more sources
In this paper, we introduce the Sasaki–Ricci flow to study the existence of η-Einstein metrics. In the positive case any η-Einstein metric can be homothetically transformed to a Sasaki–Einstein metric. Hence it is an odd-dimensional counterpart of the Kähler–Ricci flow. We prove its well-posedness and long-time existence.
Smoczyk, Knut +2 more
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Smoothing a measure on a Riemann surface using Ricci flow
, 2021We formulate and solve the existence problem for Ricci flow on a Riemann surface with initial data given by a Radon measure as volume measure. The theory leads us to a large class of new examples of nongradient expanding Ricci solitons, including the ...
P. Topping, Hao Yin
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International Journal of Mathematics, 2020
In this paper, we study the Ricci–Bourguignon flow of all locally homogenous geometries on closed three-dimensional manifolds. We also consider the evolution of the Yamabe constant under the Ricci–Bourguignon flow. Finally, we prove some results for the Bach-flat shrinking gradient soliton to the Ricci–Bourguignon flow.
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In this paper, we study the Ricci–Bourguignon flow of all locally homogenous geometries on closed three-dimensional manifolds. We also consider the evolution of the Yamabe constant under the Ricci–Bourguignon flow. Finally, we prove some results for the Bach-flat shrinking gradient soliton to the Ricci–Bourguignon flow.
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Ollivier Ricci-flow on weighted graphs
American Journal of Mathematics, 2020:We study the existence of solutions of Ricci flow equations of Ollivier-Lin-Lu-Yau curvature defined on weighted graphs. Our work is motivated by the work of Ni-Lin-Luo-Gao in which the discrete time Ricci flow algorithm has been applied successfully as
Shuliang Bai +4 more
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A modified Ricci flow on arbitrary weighted graph
Journal of Geometric AnalysisIn this paper, we propose a modified Ricci flow, as well as a quasi-normalized Ricci flow, on arbitrary weighted graph. Each of these two flows has a unique global solution.
Jicheng Ma, Yunyan Yang
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