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Related papers: Recent developments in Ricci flows

200 papers

This paper investigates the short-time existence and uniqueness of Ricci flow solutions on Finsler manifolds. The main results of this paper are theorems demonstrating the short-time existence of the flow solution for $n$-dimensional…

Differential Geometry · Mathematics 2023-04-07 Behroz Bidabad , Maral K. Sedaghat

We give biLipschitz models for the Ricci flow on some 4-manifolds (minimal surfaces of general type), exhibiting a combination of expanding and static behavior.

Differential Geometry · Mathematics 2025-01-23 John Lott

A short overview of recent developments on resummations in QCD is presented.

High Energy Physics - Phenomenology · Physics 2007-05-23 Andrea Banfi

In this note, a modified K\"ahler-Ricci flow is introduced and studied. The main point is to show the flexibility of K\"ahler-Ricci flow and summarize some useful techniques.

Differential Geometry · Mathematics 2008-01-24 Zhou Zhang

We survey several problems concerning Riemannian manifolds with positive curvature of one form or another. We describe the PIC1 notion of positive curvature and argue that it is often the sharp notion of positive curvature to consider.…

Differential Geometry · Mathematics 2023-09-04 Peter M. Topping

We explore the harmonic-Ricci flow---that is, Ricci flow coupled with harmonic map flow---both as it arises naturally in certain principal bundle constructions related to Ricci flow and as a geometric flow in its own right. We demonstrate…

Differential Geometry · Mathematics 2012-12-18 Michael Bradford Williams

In this short note, we give simple proof of the Ricci flow's local existence and uniqueness on closed Einstein manifolds. We suggest a new setting for studying the space of Riemannian metrics on a compact manifold.

Differential Geometry · Mathematics 2022-11-09 Kaveh Eftekharinasab

In this note we attempt to propose a categorical framework for the Ricci flow, treating it as a sequence of functors connecting the stack of Riemannian metrics to the category of geometric decompositions via singular flow spacetimes. To…

Category Theory · Mathematics 2026-01-27 Alexander Plakhotnikov

Using a recently developed piecewise flat method, numerical evolutions of the Ricci flow are computed for a number of manifolds, using a number of different mesh types, and shown to converge to the expected smooth behaviour as the mesh…

Differential Geometry · Mathematics 2024-02-26 Rory Conboye

We study noncommutative Ricci flow in a finite dimensional representation of a noncommutative torus. It is shown that the flow exists and converges to the flat metric. We also consider the evolution of entropy and a definition of scalar…

Mathematical Physics · Physics 2014-02-10 Rocco Duvenhage

Expository observation on the $\mu$-invariant of singularity models for Ricci Flow.

Differential Geometry · Mathematics 2011-04-19 Bennett Chow

In this work we study properties of stability and non-stability of harmonic maps under the homogeneous Ricci flow. We provide examples where the stability (non-stability) is preserved under the Ricci flow and an example where the Ricci flow…

Differential Geometry · Mathematics 2017-01-23 Rafaela F. do Prado , Lino Grama

In this paper we present several curvature estimates for solutions of the Ricci flow which depend on smallness of certain local integrals of the norm of the Riemann curvature tensor.

Differential Geometry · Mathematics 2007-07-17 Rugang Ye

We study the evolution of wormhole geometries under Ricci flow using numerical methods. Depending on values of initial data parameters, wormhole throats either pinch off or evolve to a monotonically growing state. The transition between…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Viqar Husain , Sanjeev S. Seahra

Recently, we have studied evolution of a family of Finsler metrics along Finsler Ricci flow and proved its convergence in short time. Here, existence of solutions to the so called Hamilton Ricci flow on Finsler spaces is studied and a short…

Differential Geometry · Mathematics 2015-08-13 B. Bidabad , M. K. Sedaghat

For homogeneous metrics on the spaces of the title it is shown that the Ricci flow can move a metric of stricly positive sectional curvature to one with some negative sectional curvature and one of positive definite Ricci tensor to one with…

Differential Geometry · Mathematics 2015-09-16 Man-Wai Cheung , Nolan R. Wallach

In this note, we provide some general discussion on the Ricci lower bound along K\"ahler-Ricci flow with singularity over closed manifold.

Differential Geometry · Mathematics 2011-10-28 Zhou Zhang

We give a geometric interpretation of the linear trace Harnack inequality for the Ricci flow.

Differential Geometry · Mathematics 2007-05-23 Bennett Chow , Sun-Chin Chu

In this work, we study and solve the normalized Ricci flow equation for circle bundles over surfaces. Moreover, we study the asymptotic behavior of the solutions and their connections to some model geometries.

Differential Geometry · Mathematics 2025-05-08 Arash Bazdar , Georgios Fotopoulos

In this article we study the short-time existence of conformal Ricci flow on asymptotically hyperbolic manifolds. We also prove a local Shi's type curvature derivative estimate for conformal Ricci flow.

Differential Geometry · Mathematics 2018-01-12 Peng Lu , Jie Qing , Yu Zheng