Results 1 to 10 of about 100,587 (171)

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   +7 more sources

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   +3 more sources

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

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
exaly   +4 more sources

The Ricci flow for nilmanifolds

Journal of Modern Dynamics, 2010
We consider the Ricci flow for simply connected nilmanifolds, which translates to a Ricci flow on the space of nilpotent metric Lie algebras. We consider the evolution of the inner product and the evolution of structure constants, as well as the evolution of these quantities modulo rescaling.
Tracy L Payne
exaly   +3 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

The Chern–Ricci flow

Rendiconti Lincei, Matematica e Applicazioni, 2022
We give a survey on the Chern–Ricci flow, a parabolic flow of Hermitian metrics on complex manifolds. We emphasize open problems and new directions.
Valentino Tosatti, Ben Weinkove
openaire   +3 more sources

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