Results 1 to 10 of about 100,620 (126)

High genus surface parameterization using the Euclidean Ricci flow method [PDF]

Scientific Reports
The parameterization of surfaces, which is related to many frontier problems in mathematics, has long been a challenge for scientists and engineers.
Yuan-guang Wang
doaj   +2 more sources

Deep learning as Ricci flow [PDF]

Scientific Reports
Deep neural networks (DNNs) are powerful tools for approximating the distribution of complex data. It is known that data passing through a trained DNN classifier undergoes a series of geometric and topological simplifications.
Anthony Baptista, Alessandro Barp, Tapabrata Chakraborti, Chris Harbron, Ben D. MacArthur, Christopher R. S. Banerji   +5 more
doaj   +2 more sources

Eigenvalue lower bounds and splitting for modified Ricci flow

Advanced Nonlinear Studies
We prove sharp lower bounds for eigenvalues of the drift Laplacian for a modified Ricci flow. The modified Ricci flow is a system of coupled equations for a metric and weighted volume that plays an important role in Ricci flow.
Colding Tobias Holck, Minicozzi II William P.   +1 more
doaj   +2 more sources

Ricci flow-based spherical parameterization and surface registration [PDF]

Computer Vision and Image Understanding, 2013
Huiguang He, Xianfeng Gu, Jing Hua
exaly   +2 more sources

Hyperbolic Ricci-Bourguignon-Harmonic Flow [PDF]

Mathematics Interdisciplinary Research, 2022
In this paper, we consider hyperbolic Ricci-Bourguignon flow on a compact Riemannian manifold M coupled with the harmonic map flow between M and a fixed manifold N. At the first, we prove the unique short-time existence to solution of this system.
Shahrood Azami
doaj   +1 more source

On Weak Super Ricci Flow through Neckpinch

Analysis and Geometry in Metric Spaces, 2021
In this article, we study the Ricci flow neckpinch in the context of metric measure spaces. We introduce the notion of a Ricci flow metric measure spacetime and of a weak (refined) super Ricci flow associated to convex cost functions (cost functions ...
Lakzian Sajjad, Munn Michael
doaj   +1 more source

The ∗-Ricci Operator on Hopf Real Hypersurfaces in the Complex Quadric

Mathematics, 2022
We study the ∗-Ricci operator on Hopf real hypersurfaces in the complex quadric. We prove that for Hopf real hypersurfaces in the complex quadric, the ∗-Ricci tensor is symmetric if and only if the unit normal vector field is singular.
Rongsheng Ma, Donghe Pei
doaj   +1 more source

Symmetries of Ricci flows

Advances in Nonlinear Analysis, 2023
In the present work, we find the Lie point symmetries of the Ricci flow on an n-dimensional manifold, and we introduce a method in order to reutilize these symmetries to obtain the Lie point symmetries of particular metrics.
López Enrique, Dimas Stylianos, Bozhkov Yuri   +2 more
doaj   +1 more source

Evolution for First Eigenvalue of L_T,f on an Evolving Riemannian Manifold

Mathematics, 2022
In this paper, evolution formulas for the first non-zero eigenvalue of the operator LT,f on a weighted closed Riemannian manifold along the Ricci flow as well as along the Yamabe flow are formulated.
Apurba Saha, Shahroud Azami, Daniel Breaz, Eleonora Rapeanu, Shyamal Kumar Hui   +4 more
doaj   +1 more source

Eigenvalues and entropies under the harmonic-Ricci flow [PDF]

, 2013
In this paper, the author discusses the eigenvalues and entropies under the harmonic-Ricci flow, which is the Ricci flow coupled with the harmonic map flow. We give an alternative proof of results for compact steady and expanding harmonic-Ricci breathers.
Li, Yi
core   +2 more sources