scholarly journals Long time existence and bounded scalar curvature in the Ricci-harmonic flow

2018 ◽  
Vol 265 (1) ◽  
pp. 69-97 ◽  
Author(s):  
Yi Li
Keyword(s):  
Scalar Curvature ◽  
Long Time Existence ◽  
Long Time ◽  
Harmonic Flow ◽  
Time Existence

scholarly journals Long time existence of hyperbolic Ricci-Bourguignon flow on Riemannian Surfaces

2020 ◽  
Vol 26 (2) ◽  
pp. 202-212
Author(s):  
Mehrad Mohammadi ◽  
Shahroud Azami
Keyword(s):  
Scalar Curvature ◽  
Classical Solution ◽  
Necessary Condition ◽  
Global Classical Solution ◽  
Long Time Existence ◽  
Riemannian Surfaces ◽  
Long Time ◽  
Time Existence ◽  
Sufficient And Necessary Condition

We consider the hyperbolic Ricci-Bourguignon flow(HRBF) equation on Riemannian surfaces and we find a sufficient and necessary condition to this flow has global classical solution. Also, we show that the scalar curvature of the solution metric gij convergence to the flat curvature.

scholarly journals Long time existence of Ricci-harmonic flow

2016 ◽  
Vol 11 (5) ◽  
pp. 1313-1334 ◽  
Author(s):  
Yi Li
Keyword(s):  
Long Time Existence ◽  
Long Time ◽  
Harmonic Flow ◽  
Time Existence

THE LONG-TIME EXISTENCE AND CONVERGENCE OF THE CR YAMABE FLOW

2012 ◽  
Vol 14 (02) ◽  
pp. 1250014 ◽  
Author(s):  
PAK TUNG HO
Keyword(s):  
Scalar Curvature ◽  
Sectional Curvature ◽  
Contact Form ◽  
Cr Manifold ◽  
Yamabe Flow ◽  
Long Time Existence ◽  
Long Time ◽  
Standard Contact ◽  
Time Existence ◽  
Cr Yamabe Flow

In this paper, we prove the long-time existence of the CR Yamabe flow on the compact strictly pseudoconvex CR manifold with positive CR invariant. We also prove the convergence of the CR Yamabe flow on the sphere by proving that: the contact form which is pointwise conformal to the standard contact form on the sphere converges exponentially to a contact form of constant pseudo-Hermitian sectional curvature. We also show that the eigenvalues of some geometric operators are non-decreasing under the unnormalized CR Yamabe flow provided that the pseudo-Hermitian scalar curvature satisfies certain conditions.

scholarly journals Long-Time Existence for Semi-linear Beam Equations on Irrational Tori

2021 ◽  
Author(s):  
Joackim Bernier ◽  
Roberto Feola ◽  
Benoît Grébert ◽  
Felice Iandoli
Keyword(s):  
Long Time Existence ◽  
Beam Equations ◽  
Long Time ◽  
Time Existence

scholarly journals Long-time existence for semilinear wave equations with the inverse-square potential

2022 ◽  
Vol 309 ◽  
pp. 98-141
Author(s):  
Wei Dai ◽  
Daoyuan Fang ◽  
Chengbo Wang
Keyword(s):  
Wave Equations ◽  
Semilinear Wave Equations ◽  
Long Time Existence ◽  
Long Time ◽  
Time Existence

Evolving inextensible and elastic curves with clamped ends under the second-order evolution equation in ℝ2

2018 ◽  
Vol 3 (1) ◽  
pp. 14-18 ◽  
Author(s):  
Chun-Chi Lin ◽  
Yang-Kai Lue
Keyword(s):  
Evolution Equation ◽  
Convergent Subsequence ◽  
Second Order ◽  
Plane Curves ◽  
Smooth Solutions ◽  
Fixed Position ◽  
Elastic Curves ◽  
Long Time Existence ◽  
Long Time ◽  
Time Existence

Abstract For any given C2-smooth initial open curves with fixed position and fixed tangent at the boundary points, we obtain the long-time existence of smooth solutions under the second-order evolution of plane curves. Moreover, the asymptotic limit of a convergent subsequence is an inextensible elastica.

scholarly journals Long-time existence of the edge Yamabe flow

2019 ◽  
Vol 71 (2) ◽  
pp. 651-688 ◽  
Author(s):  
Eric BAHUAUD ◽  
Boris VERTMAN
Keyword(s):  
Yamabe Flow ◽  
Long Time Existence ◽  
Long Time ◽  
Time Existence
Sign in / Sign up

Export Citation Format

Share Document