scholarly journals A no expanding breather theorem for noncompact Ricci flows

2022 ◽  
Author(s):  
Liang Cheng ◽  
Yongjia Zhang
Keyword(s):  
Ricci Flows

Combinatorial p-th Ricci flows on surfaces

2021 ◽  
Vol 211 ◽  
pp. 112417
Author(s):  
Aijin Lin ◽  
Xiaoxiao Zhang
Keyword(s):  
Ricci Flows ◽  
Flows On Surfaces

scholarly journals Nonholonomic Ricci flows. II. Evolution equations and dynamics

2008 ◽  
Vol 49 (4) ◽  
pp. 043504 ◽  
Author(s):  
Sergiu I. Vacaru
Keyword(s):  
Evolution Equations ◽  
Ricci Flows

scholarly journals Perelman's entropy on ancient Ricci flows

2021 ◽  
pp. 109195
Author(s):  
Zilu Ma ◽  
Yongjia Zhang
Keyword(s):  
Ricci Flows

scholarly journals Ricci flows with unbounded curvature

2012 ◽  
Vol 273 (1-2) ◽  
pp. 449-460 ◽  
Author(s):  
Gregor Giesen ◽  
Peter M. Topping
Keyword(s):  
Ricci Flows

scholarly journals Almost-rigidity and the extinction time of positively curved Ricci flows

2016 ◽  
Vol 369 (1-2) ◽  
pp. 899-911 ◽  
Author(s):  
Richard H. Bamler ◽  
Davi Maximo
Keyword(s):  
Extinction Time ◽  
Ricci Flows ◽  
Positively Curved ◽  
Almost Rigidity

scholarly journals Combinatorial Ricci Flows on Surfaces

2003 ◽  
Vol 63 (1) ◽  
pp. 97-129 ◽  
Author(s):  
Bennett Chow ◽  
Feng Luo
Keyword(s):  
Ricci Flows ◽  
Flows On Surfaces

scholarly journals METRIC COMPATIBLE OR NON-COMPATIBLE FINSLER–RICCI FLOWS

2012 ◽  
Vol 09 (05) ◽  
pp. 1250041 ◽  
Author(s):  
SERGIU I. VACARU
Keyword(s):  
Ricci Flow ◽  
Evolution Equations ◽  
Finsler Geometry ◽  
Flow Theory ◽  
Finsler Metric ◽  
Geometric Evolution ◽  
Ricci Flows ◽  
Canonical Metric ◽  
Self Consistent ◽  
Math Phys

There were elaborated different models of Finsler geometry using the Cartan (metric compatible), or Berwald and Chern (metric non-compatible) connections, the Ricci flag curvature, etc. In a series of works, we studied (non)-commutative metric compatible Finsler and non-holonomic generalizations of the Ricci flow theory [see S. Vacaru, J. Math. Phys. 49 (2008) 043504; 50 (2009) 073503 and references therein]. The aim of this work is to prove that there are some models of Finsler gravity and geometric evolution theories with generalized Perelman's functionals, and correspondingly derived non-holonomic Hamilton evolution equations, when metric non-compatible Finsler connections are involved. Following such an approach, we have to consider distortion tensors, uniquely defined by the Finsler metric, from the Cartan and/or the canonical metric compatible connections. We conclude that, in general, it is not possible to elaborate self-consistent models of geometric evolution with arbitrary Finsler metric non-compatible connections.

scholarly journals Optimal Curvature Estimates for Homogeneous Ricci Flows

2017 ◽  
Vol 2019 (14) ◽  
pp. 4431-4468 ◽  
Author(s):  
Christoph Böhm ◽  
Ramiro Lafuente ◽  
Miles Simon
Keyword(s):  
Homogeneous Space ◽  
Homogeneous Spaces ◽  
Convergence Result ◽  
Einstein Metric ◽  
Type I ◽  
Extinction Time ◽  
Ricci Flows ◽  
Gap Theorem ◽  
Ancient Solutions ◽  
Curvature Estimates

AbstractWe prove uniform curvature estimates for homogeneous Ricci flows: For a solution defined on $[0,t]$ the norm of the curvature tensor at time $t$ is bounded by the maximum of $C(n)/t$ and $C(n)({\mathrm{scal}}(g(t)) - {\mathrm{scal}}(g(0)) )$. This is used to show that solutions with finite extinction time are Type I, immortal solutions are Type III and ancient solutions are Type I, with constants depending only on the dimension $n$. A further consequence is that a non-collapsed homogeneous ancient solution on a compact homogeneous space emerges from a unique Einstein metric on that space. The above curvature estimates follow from a gap theorem for Ricci-flatness on homogeneous spaces. This theorem is proved by contradiction, using a local $W^{2,p}$ convergence result which holds without symmetry assumptions.

Smooth structures, normalized Ricci flows, and finite cyclic groups

2008 ◽  
Vol 35 (3) ◽  
pp. 267-275 ◽  
Author(s):  
Masashi Ishida ◽  
Ioana Şuvaina
Keyword(s):  
Cyclic Groups ◽  
Smooth Structures ◽  
Ricci Flows
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