scholarly journals Gradient flows on nonpositively curved metric spaces and harmonic maps

1998 ◽  
Vol 6 (2) ◽  
pp. 199-253 ◽  
Author(s):  
Uwe F. Mayer
Keyword(s):  
Metric Spaces ◽  
Harmonic Maps ◽  
Gradient Flows ◽  
Nonpositively Curved

scholarly journals UNIQUENESS THEOREMS FOR HARMONIC MAPS INTO METRIC SPACES

2002 ◽  
Vol 04 (04) ◽  
pp. 725-750 ◽  
Author(s):  
CHIKAKO MESE
Keyword(s):  
Riemannian Manifolds ◽  
Metric Space ◽  
Metric Spaces ◽  
Harmonic Maps ◽  
Uniqueness Theorems ◽  
Singular Spaces ◽  
Domain Space ◽  
Recent Developments

Recent developments extend much of the known theory of classical harmonic maps between smooth Riemannian manifolds to the case when the target is a metric space of curvature bounded from above. In particular, the existence and regularity theorems for harmonic maps into these singular spaces have been successfully generalized. Furthermore, the uniqueness of harmonic maps is known when the domain has a boundary (with a smallness of image condition if the target curvature is bounded from above by a positive number). In this paper, we will address the question of uniqueness when the domain space is without a boundary in two cases: one, when the curvature of the target is strictly negative and two, for a map between surfaces with nonpositive target curvature.

Γ-convergence and relaxations for gradient flows in metric spaces: a minimizing movement approach

2019 ◽  
Vol 25 ◽  
pp. 28
Author(s):  
Florentine Fleißner
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Gradient Flow ◽  
Gradient Flows ◽  
Flow Motion ◽  
Limit Functional ◽  
Γ Convergence

We present new abstract results on the interrelation between the minimizing movement scheme for gradient flows along a sequence of Γ-converging functionals and the gradient flow motion for the corresponding limit functional, in a general metric space. We are able to allow a relaxed form of minimization in each step of the scheme, and so we present new relaxation results too.

scholarly journals The Systems of Nonlinear Gradient Flows on Metric Spaces and Its Gamma-Convergence

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Mao-Sheng Chang ◽  
Bo-Cheng Lu
Keyword(s):  
Nonlinear System ◽  
Metric Spaces ◽  
Gradient Flow ◽  
Gamma Convergence ◽  
Gradient Flows ◽  
Energy Functionals ◽  
Several Variables ◽  
Flow Systems

We first establish the explicit structure of nonlinear gradient flow systems on metric spaces and then develop Gamma-convergence of the systems of nonlinear gradient flows, which is a scheme meant to ensure that if a family of energy functionals of several variables depending on a parameter Gamma-converges, then the solutions to the associated systems of gradient flows converge as well. This scheme is a nonlinear system edition of the notion initiated by Sylvia Serfaty in 2011.

scholarly journals Weighted Energy-Dissipation principle for gradient flows in metric spaces

2019 ◽  
Vol 127 ◽  
pp. 1-66 ◽  
Author(s):  
Riccarda Rossi ◽  
Giuseppe Savaré ◽  
Antonio Segatti ◽  
Ulisse Stefanelli
Keyword(s):  
Energy Dissipation ◽  
Metric Spaces ◽  
Gradient Flows ◽  
Weighted Energy
Sign in / Sign up

Export Citation Format

Share Document