Results 1 to 10 of about 5,292,102 (148)

Matrix Li-Yau-Hamilton estimates under Ricci flow and parabolic frequency. [PDF]

Calc Var Partial Differ Equ, 2023
We prove matrix Li–Yau–Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the Ricci flow.
Li X, Zhang QS.
europepmc   +3 more sources

Community Detection on Networks with Ricci Flow. [PDF]

Sci Rep, 2019
Many complex networks in the real world have community structures – groups of well-connected nodes with important functional roles. It has been well recognized that the identification of communities bears numerous practical applications.
Ni CC, Lin YY, Luo F, Gao J.
europepmc   +3 more sources

Charting cellular differentiation trajectories with Ricci flow

Nature Communications, 2023
Complex biological processes, such as cellular differentiation, require intricate rewiring of intra-cellular signalling networks. Previous characterisations revealed a raised network entropy underlies less differentiated and malignant cell states.
Anthony Baptista, Ben D. MacArthur, Christopher R. S. Banerji   +2 more
doaj   +2 more sources

Cobordism, singularities and the Ricci flow conjecture [PDF]

Journal of High Energy Physics, 2023
In the following work, an attempt to conciliate the Ricci flow conjecture and the Cobordism conjecture, stated as refinements of the Swampland distance conjecture and of the No global symmetries conjecture respectively, is presented.
David Martín Velázquez, Davide De Biasio, Dieter Lüst   +2 more
doaj   +2 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

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

The Heterotic-Ricci Flow and Its Three-Dimensional Solitons [PDF]

Journal of Geometric Analysis, 2023
We introduce a novel curvature flow, the Heterotic-Ricci flow, as the two-loop renormalization group flow of the Heterotic string common sector and study its three-dimensional compact solitons.
Andrei Moroianu, Á. Murcia, C. Shahbazi
semanticscholar   +1 more source

Gap Theorem on Riemannian manifolds using Ricci flow [PDF]

Advances in Mathematics, 2023
In this work, we use the Ricci flow approach to study the gap phenomenon of Riemannian manifolds with non-negative curvature and sub-critical scaling invariant curvature decay.
Pak-Yeung Chan, Man-Chun Lee
semanticscholar   +1 more source

Ricci Flow-based Spherical Parameterization and Surface Registration. [PDF]

Comput Vis Image Underst, 2013
Chen X, He H, Zou G, Zhang X, Gu X, Hua J.   +5 more
europepmc   +2 more sources