Related papers: Teichm\"uller harmonic map flow into nonpositively…

In this paper, by combining techniques from Ricci flow and algebraic geometry, we prove the following generalization of the classical uniformization theorem of Riemann surfaces. Given a complete noncompact complex two dimensional K\"ahler…

We develop an abstract theory of flows of geometric $H$-structures, i.e., flows of tensor fields defining $H$-reductions of the frame bundle, for a closed and connected subgroup $H\subset SO(n)$, on any connected and oriented $n$-manifold…

Let $S$ be a closed, genus $g$ surface. The space of geodesic currents on $S$ encompasses the set of closed curves up to homotopy, as well as Teichm\"uller space, and many other spaces of structures on $S$. We show that one can define a…

In this article we introduce a natural extension of the well-studied equation for harmonic maps between Riemannian manifolds by assuming that the target manifold is equipped with a connection that is metric but has non-vanishing torsion.…

Let $(M, \mathcal{F})$ be a compact Riemannian foliated manifold. We consider a family of compatible Feller semigroups in $C(M^n)$ associated to laws of the $n$-point motion. Under some assumptions (Le Jan and Raimond, \cite{Le…

We deform a map into a Riemannian manifold that is horizontal with respect to a submersion onto a non-positively curved manifold and satisfies a Chow condition into a harmonic one through a horizontal homotopy.

We show the existence of non-trivial self-expanding harmonic map flows starting from non-energy-minimizing 0-homogeneous maps to a regular ball or a closed hemisphere. In particular, given a non-minimizing but stationary 0-homogeneous…

In this paper, we consider the solutions of the relaxed Q-tensor flow in $\R^3$ with small parameter $\epsilon$. Firstly, we show that the limiting map is the so called harmonic map flow; Secondly, we also present a new proof for the global…

We consider the problem of deforming a one-parameter family of hypersurfaces immersed into closed Riemannian manifolds with positive curvature operator. The hypersurface in this family satisfies mean curvature flow while the ambient metric…

We extend the DeTurck trick from the classical isotropic curve shortening flow to the anisotropic setting. Here the anisotropic energy density is allowed to depend on space, which allows an interpretation in the context of Finsler metrics,…

We investigate the blow-up analysis and quantitative behavior for a sequence of maps $\{u_n\}_{n=1}^\infty$ from degenerating tori $(T^2,g_n)$ or from degenerating cylinders $(S^1\times [0,\pi],g_n)$ with free boundary conditions…

We prove a regularity theorem for harmonic maps into Teichm\"uller space. More specifically, if $u$ is a harmonic map from a Riemannian domain to the metric completion of Teichm\"uller space with respect to the Weil-Petersson metric, and…

We prove a quantitative version of the non-uniform hyperbolicity of the Teichm\"uller geodesic flow. Namely, at each point of any Teichm\"uller flow line, we bound the infinitesimal spectral gap for variations of the Hodge norm along the…

We investigate a new geometric flow which consists of a coupled system of the Ricci flow on a closed manifold M with the harmonic map flow of a map phi from M to some closed target manifold N with a (possibly time-dependent) positive…

In this paper, we propose a new numerical scheme for a spatially discrete model of constrained total variation flows, which are total variation flows whose values are constrained in a Riemannian manifold. The difficulty of this problem is…

We prove that for any open Riemann surface $N,$ natural number $n\geq 3,$ non-constant harmonic map $h:N\to \mathbb{R}^{n-2}$ and holomorphic 2-form $H$ on $N,$ there exists a weakly complete harmonic map $X=(X_j)_{j=1,\ldots,n}:N \to…

We consider harmonic maps on simply connected Riemann surfaces into the group $\mathrm{U}(n)$ of unitary matrices of order $n$. It is known that a harmonic map with an associated algebraic extended solution can be deformed into a new…

In this paper, we consider the heat flow for p-pseudoharmonic maps from a closed Sasakian manifold M into a compact Riemannian manifold N. We prove global existence and asymptotic convergence of the solution for the p-pseudoharmonic map…

The results of this paper are twofold: In the first part, we prove that for Schr\"odinger map flows from hyperbolic planes to Riemannian surfaces with non-positive sectional curvatures, the harmonic maps which are holomorphic or…

The Teichm\"{u}ller curve is the fiber space over Teichm\"{u}ller space of closed Riemann surfaces, where the fiber over a point in Teichm\"{u}ller space is the underlying surface. We derive formulas for sectional curvatures on the…