Results 11 to 20 of about 120,930 (291)

Trace anomaly, Perelman’s functionals and the cosmological constant [PDF]

Classical and quantum gravity, 2021
The trace anomaly and the cosmological constant problem are two typical breakdowns when applying the quantum principle to a general covariant or gravitational system. A quantum theory of spacetime reference frame is proposed and reviewed.
M. Luo
semanticscholar   +1 more source

Differential Harnack estimates for a weighted nonlinear parabolic equation under a super Perelman–Ricci flow and implications

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2023
In this paper, we derive new differential Harnack estimates of Li–Yau type for positive smooth solutions to a class of nonlinear parabolic equations in the form \[ {\mathscr L}_\phi^{\mathsf a} [w]:= \left[ \frac{\partial}{\partial t} - \mathsf{a}(x ...
Ali Taheri, Vahideh Vahidifar
semanticscholar   +1 more source

Gradient Estimates for a Weighted Γ-nonlinear Parabolic Equation Coupled with a Super Perelman-Ricci Flow and Implications

Potential Analysis, 2021
This article studies a nonlinear parabolic equation on a complete weighted manifold where the metric and potential evolve under a super Perelman-Ricci flow.
A. Taheri
semanticscholar   +1 more source

Perelman’s Ricci Flow in topological quantum gravity [PDF]

Advances in Theoretical and Mathematical Physics, 2020
We find the regime of our recently constructed topological nonrelativistic quantum gravity, in which Perelman's Ricci flow equations on Riemannian manifolds appear precisely as the localization equations in the path integral.
A. Frenkel, Petr Hořava, Stephen Randall   +2 more
semanticscholar   +1 more source

Off-diagonal cosmological solutions in emergent gravity theories and Grigory Perelman entropy for geometric flows

The European Physical Journal C, 2021
We develop an approach to the theory of relativistic geometric flows and emergent gravity defined by entropy functionals and related statistical thermodynamics models. Nonholonomic deformations of G.
S. Vacaru, E. V. Veliev, L. Bubuianu
semanticscholar   +1 more source

Perelman-type no breather theorem for noncompact Ricci flows [PDF]

, 2020
In this paper, we first show that a complete shrinking breather with Ricci curvature bounded from below must be a shrinking gradient Ricci soliton. This result has several applications.
Liang Cheng, Yongjia Zhang
semanticscholar   +1 more source

Geometric information flows and G. Perelman entropy for relativistic classical and quantum mechanical systems [PDF]

The European Physical Journal C, 2019
This work consists an introduction to the classical and quantum information theory of geometric flows of (relativistic) Lagrange–Hamilton mechanical systems.
S. Vacaru
semanticscholar   +1 more source

Perelman’s entropies for manifolds with conical singularities [PDF]

Transactions of the American Mathematical Society, 2019
In this paper we discuss Perelman's Lambda-functional, Perelman's Ricci shrinker entropy as well as the Ricci expander entropy on a class of manifolds with isolated conical singularities.
Klaus Kroencke, Boris Vertman
semanticscholar   +1 more source

A Note on Perelman’s No Shrinking Breather Theorem [PDF]

Journal of Geometric Analysis, 2018
As an application of his entropy formula, Perelman (The entropy formula for the Ricci flow and its geometric applications, 2002) proved that every compact shrinking breather solution to the Ricci flow is a shrinking gradient Ricci soliton. Zhang (Asian J
Yongjia Zhang
semanticscholar   +1 more source

Un enigma llamado Grigori Perelman

Revista de Educación Matemática, 2021
La famosa Conjetura de Poincaré (1904), de enunciado puramente topológico, fue probada por el matemático ruso Grigori Perelman en el 2002 usando geometría y ecuaciones diferenciales.
Jorge Lauret
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