Ricci-Bourguignon flow coupled with harmonic map flow

2019 ◽  
Vol 30 (10) ◽  
pp. 1950049 ◽  
Author(s):  
Shahroud Azami
Keyword(s):  
Riemannian Manifold ◽  
Existence And Uniqueness ◽  
Harmonic Map ◽  
Coupled System ◽  
Geometric Structures ◽  
Closed Riemannian Manifold ◽  
Harmonic Map Flow

In this paper, we study a coupled system of the Ricci–Bourguignon flow on a closed Riemannian manifold [Formula: see text] with the harmonic map flow. At the first, we will investigate the existence and uniqueness for solution of this flow on a closed Riemannian manifold and then we find evolution of some geometric structures of manifold along this flow.

scholarly journals Convergence of the solutions of discounted Hamilton–Jacobi systems

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Andrea Davini ◽  
Maxime Zavidovique
Keyword(s):  
Riemannian Manifold ◽  
Coupled System ◽  
Discount Factor ◽  
Limit System ◽  
Specific Solution ◽  
Closed Riemannian Manifold ◽  
Weakly Coupled ◽  
Weakly Coupled System ◽  
Jacobi Equations ◽  
Minimizing Measures

Abstract We consider a weakly coupled system of discounted Hamilton–Jacobi equations set on a closed Riemannian manifold. We prove that the corresponding solutions converge to a specific solution of the limit system as the discount factor goes to 0. The analysis is based on a generalization of the theory of Mather minimizing measures for Hamilton–Jacobi systems and on suitable random representation formulae for the discounted solutions.

scholarly journals Perturbations of the Harmonic Map Equation

2003 ◽  
Vol 05 (04) ◽  
pp. 629-669 ◽  
Author(s):  
T. Kappeler ◽  
S. Kuksin ◽  
V. Schroeder
Keyword(s):  
Riemannian Manifold ◽  
Sectional Curvature ◽  
Homotopy Class ◽  
Harmonic Map ◽  
Poincaré Inequality ◽  
Classical Solutions ◽  
Important Ingredient ◽  
Closed Riemannian Manifold ◽  
Nonpositive Sectional Curvature ◽  
Target Manifold

We consider perturbations of the harmonic map equation in the case where the target manifold is a closed Riemannian manifold of nonpositive sectional curvature. For any semilinear and, under some extra conditions, quasilinear perturbation, the space of classical solutions within a homotopy class is proved to be compact. An important ingredient for our analysis is a new inequality for maps in a given homotopy class which can be viewed as a version of the Poincaré inequality for such maps.

Infinite time blow-up for half-harmonic map flow from R into S1

2021 ◽  
Vol 143 (4) ◽  
pp. 1261-1335
Author(s):  
Yannick Sire ◽  
Juncheng Wei ◽  
Youquan Zheng
Keyword(s):  
Blow Up ◽  
Harmonic Map ◽  
Infinite Time ◽  
Harmonic Map Flow

scholarly journals Uniqueness and nonuniqueness of limits of Teichmüller harmonic map flow

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
James Kohout ◽  
Melanie Rupflin ◽  
Peter M. Topping
Keyword(s):  
Constant Curvature ◽  
Harmonic Map ◽  
Gradient Flow ◽  
Minimal Immersion ◽  
Curvature Surface ◽  
Previous Theory ◽  
Target Manifold ◽  
Harmonic Map Flow

AbstractThe harmonic map energy of a map from a closed, constant-curvature surface to a closed target manifold can be seen as a functional on the space of maps and domain metrics. We consider the gradient flow for this energy. In the absence of singularities, previous theory established that the flow converges to a branched minimal immersion, but only at a sequence of times converging to infinity, and only after pulling back by a sequence of diffeomorphisms. In this paper, we investigate whether it is necessary to pull back by these diffeomorphisms, and whether the convergence is uniform as {t\to\infty}.

scholarly journals Some results on stable p-harmonic maps

1994 ◽  
Vol 36 (1) ◽  
pp. 77-80 ◽  
Author(s):  
Leung-Fu Cheung ◽  
Pui-Fai Leung
Keyword(s):  
Riemannian Manifold ◽  
Critical Point ◽  
Harmonic Maps ◽  
Harmonic Map ◽  
Energy Functional ◽  
Complete Riemannian Manifold ◽  
Image Position ◽  
Simply Connected

For each p ∈ [2, ∞)a p-harmonic map f:Mm→Nn is a critical point of the p-energy functionalwhere Mm is a compact and Nn a complete Riemannian manifold of dimensions m and n respectively. In a recent paper [3], Takeuchi has proved that for a certain class of simply-connected δ-pinched Nn and certain type of hypersurface Nn in ℝn+1, the only stable p-harmonic maps for any compact Mm are the constant maps. Our purpose in this note is to establish the following theorem which complements Takeuchi's results.

scholarly journals Moving mesh for the axisymmetric harmonic map flow

2005 ◽  
Vol 39 (4) ◽  
pp. 781-796
Author(s):  
Benoit Merlet ◽  
Morgan Pierre
Keyword(s):  
Harmonic Map ◽  
Moving Mesh ◽  
Harmonic Map Flow

On the Inner Radius of a Nodal Domain

2008 ◽  
Vol 51 (2) ◽  
pp. 249-260 ◽  
Author(s):  
Dan Mangoubi
Keyword(s):  
Riemannian Manifold ◽  
Lower Bounds ◽  
Type Inequality ◽  
Large Eigenvalue ◽  
Upper And Lower Bounds ◽  
Local Behavior ◽  
Nodal Domain ◽  
Closed Riemannian Manifold ◽  
Inner Radius

AbstractLet M be a closed Riemannian manifold. We consider the inner radius of a nodal domain for a large eigenvalue λ. We give upper and lower bounds on the inner radius of the type C/λα(log λ)β. Our proof is based on a local behavior of eigenfunctions discovered by Donnelly and Fefferman and a Poincaré type inequality proved by Maz’ya. Sharp lower bounds are known only in dimension two. We give an account of this case too.

scholarly journals Asymptotics of the Teichmüller harmonic map flow

2013 ◽  
Vol 244 ◽  
pp. 874-893 ◽  
Author(s):  
Melanie Rupflin ◽  
Peter M. Topping ◽  
Miaomiao Zhu
Keyword(s):  
Harmonic Map ◽  
Harmonic Map Flow

scholarly journals Hyers–Ulam stability of a coupled system of fractional differential equations of Hilfer–Hadamard type

2019 ◽  
Vol 52 (1) ◽  
pp. 283-295 ◽  
Author(s):  
Manzoor Ahmad ◽  
Akbar Zada ◽  
Jehad Alzabut
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Ulam Stability ◽  
Fractional Differential System ◽  
Different Types ◽  
Fractional Differential

AbstractIn this paper, existence and uniqueness of solution for a coupled impulsive Hilfer–Hadamard type fractional differential system are obtained by using Kransnoselskii’s fixed point theorem. Different types of Hyers–Ulam stability are also discussed.We provide an example demonstrating consistency to the theoretical findings.

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