Zobrazeno 1 - 10
of 95
pro vyhledávání: '"Rupflin, Melanie"'
Autor:
Rupflin, Melanie
As the energy of any map $v$ from $S^2$ to $S^2$ is at least $4\pi \vert deg(v)\vert$ with equality if and only if $v$ is a rational map one might ask whether maps with small energy defect $\delta_v=E(v)-4\pi \vert deg(v)\vert$ are necessarily close
Externí odkaz:
http://arxiv.org/abs/2305.17045
Autor:
Rupflin, Melanie
We consider the energy spectrum $\Xi_E(N)$ of harmonic maps from the sphere into a closed Riemannian manifold $N$. While a well known conjecture asserts that $\Xi_E(N)$ is discrete whenever $N$ is analytic, for most analytic targets it is only known
Externí odkaz:
http://arxiv.org/abs/2303.00389
Autor:
Rupflin, Melanie
We prove a sharp criterion on the decay of the tension of almost harmonic maps from degenerating surfaces that ensures that such maps subconverge to a limiting object that is made up entirely of harmonic maps.
Externí odkaz:
http://arxiv.org/abs/2210.13367
Autor:
Rupflin, Melanie
We prove Lojasiewicz inequalities for the harmonic map energy for maps from surfaces of positive genus into general analytic target manifolds which are close to simple bubble trees and as a consequence obtain new results on the convergence of harmoni
Externí odkaz:
http://arxiv.org/abs/2101.05527
In this paper we prove a gap phenomenon for critical points of the $H$-functional on closed non-spherical surfaces when $H$ is constant, and in this setting furthermore prove that sequences of almost critical points satisfy {\L}ojasiewicz inequalitie
Externí odkaz:
http://arxiv.org/abs/2007.07017
The 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
Externí odkaz:
http://arxiv.org/abs/1909.06422
Autor:
Robertson, Craig, Rupflin, Melanie
We consider the question of whether solutions of variants of Teichm\"uller harmonic map flow from surfaces $M$ to general targets can degenerate in finite time. For the original flow from closed surfaces of genus at least $2$, as well as the flow fro
Externí odkaz:
http://arxiv.org/abs/1807.06363
Autor:
Rupflin, Melanie
We discuss an alternative approach to the uniformisation problem on surfaces with boundary by representing conformal structures on surfaces $M$ of general type by hyperbolic metrics with boundary curves of constant positive geodesic curvature. In con
Externí odkaz:
http://arxiv.org/abs/1807.04464
Autor:
Große, Nadine, Rupflin, Melanie
We discuss bases of the space of holomorphic quadratic differentials that are dual to the differentials of Fenchel-Nielsen coordinates and hence appear naturally when considering functions on the set of hyperbolic metrics which are invariant under pu
Externí odkaz:
http://arxiv.org/abs/1806.04384
Autor:
Rupflin, Melanie, Topping, Peter M.
Publikováno v:
Analysis & PDE 12 (2019) 815-842
We analyse finite-time singularities of the Teichm\"uller harmonic map flow -- a natural gradient flow of the harmonic map energy -- and find a canonical way of flowing beyond them in order to construct global solutions in full generality. Moreover,
Externí odkaz:
http://arxiv.org/abs/1709.01881