Related papers: Uniform Lipschitz extension in bounded curvature

In this paper, inspired by the work Lee-Wan, we researched the rigidity of contracting maps between closed manifolds with positive curvature. We focused on the relation between curvature pinching and contracting conditions involving…

We study discrete curvatures computed from nets of curvature lines on a given smooth surface, and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties…

Functions, uniformly bounded in $BV$ norm in some bounded open set $U$ in $R^n$, are compact in $L_1(U)$. This result is known when $U$ has Lipschitz boundary [EG Th. 4 p. 176], [G 1.19 Th. p. 17], [Z 5.34 Cor. p. 227]; the proof for…

We prove the No Invariant Line Fields conjecture for a class of generalized postcritically-finite branched covers on higher-dimensional Riemannian manifolds. Moreover, we establish a quasisymmetric uniformization theorem for this class of…

We present the theory of non-stationary normal forms for uniformly contracting smooth extensions with sufficiently narrow Mather spectrum. We give coherent proofs of existence, (non)uniqueness, and a description of the centralizer results.…

We show that any space with a positive upper curvature bound has in a small neighborhood of any point a closely related metric with a negative upper curvature bound.

We prove a compactness result for capillary hypersurfaces with mean curvature prescribed by ambient functions, which generalizes the results of Sch\"atzle and Bellettini to the capillary case. The proof relies on extending the definition of…

We give a proof of the fact that the upper and the lower sectional curvature bounds of a complete manifold vary at a bounded rate under the Ricci flow.

A $1$-Lipschitz map $f$ from a convex compact set to itself has fixed points. This consequence of Brouwer's or Schauder's fixed point theorem has more elementary proofs by approximating $f$ by $\lambda$-contractions, $f_\lambda$. We study…

We study compact complex 3-manifolds admitting holomorphic Riemannian metrics. We prove a uniformization result: up to a finite unramified cover, such a manifold admits a holomorphic Riemannian metric of constant sectionnal curvature.

The existence of closed hypersurfaces of prescribed curvature in semi-riemannian manifolds is proved provided there are barriers.

We give a sufficient criterion, which we call stability, for a coarse Lipschitz map $f$ from a complete manifold $X$ with Ricci curvature bounded below to a proper Hadamard space $Y$ to be within bounded distance of a harmonic map. We prove…

We study unimodular measures on the space $\mathcal M^d$ of all pointed Riemannian $d$-manifolds. Examples can be constructed from finite volume manifolds, from measured foliations with Riemannian leaves, and from invariant random subgroups…

We review Heisenberg homology of configurations in once bounded surfaces and extend the construction to the regular thickening of a finite graph with ribbon structure.

We provide the details of the first proof in~\cite{CJS89}, which proved that Cauchy transform of $L^2$~functions on Lipschitz curves is bounded. We then prove that every $L^2$~function on Lipschitz curves is the sum of non-tangential…

We proof existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two…

We show the absolute continuity of the spectrum and determine the spectrum as a set for two classes of Hadamard manifolds and for specific domains and quotients of one of the classes.

We obtain a Landau -- Hadamard type inequality for mappings defined on the whole real axis and taking values in Riemannian manifolds. In terms of an auxiliary convex function, we find conditions under which the boundedness of covariant…

In this work, we obtain contraction results for a class of diagrams of ring morphisms which strictly includes the ones obtained by Lipman. Further, we present some applications on quotient and in the changing of the base ring in the…

We study the ends of a generic manifold, with respect to a unimodular measure on the space of pointed Riemannian manifolds with bounded curvatures. We apply our general result to the case of surfaces and obtain as corollaries a very precise…