相关论文: Superrigidity, generalized harmonic maps and unifo…
This work builds on the foundation laid by Gordon and Wilson in the study of isometry groups of solvmanifolds, i.e. Riemannian manifolds admitting a transitive solvable group of isometries. We restrict ourselves to a natural class of…
We prove that every smooth action of Z^k, k>1, on the (k+1)-dimensional torus homotopic to an action by hyperbolic linear maps preserves an absolutely continuous measure. This is a first known result concerning abelian groups of…
We establish character rigidity for all non-uniform higher-rank irreducible lattices in semisimple groups of characteristic other than 2. This implies stabilizer rigidity for probability measure preserving actions and rigidity of invariant…
We prove the holomorphic rigidity conjecture of Teichm\"{u}ller space which loosely speaking states that the action of the mapping class group uniquely determines the Teichm\"{u}ller space as a complex manifold. The method of proof is…
We prove the rigidity of presymplectic actions of a compact semisimple Lie algebra on a presymplectic manifold of constant rank in the local and global case. The proof uses an abstract normal form theorem we had stated in a previous work,…
We prove that every topological action of a countable group on a metrizable space can be realized as a bi-Lipschitz action with respect to some compatible metric. This extends a result due to U. Hamenst\"{a}dt regarding finitely generated…
We study metrics on two-dimensional simplicial complexes that are conformal either to flat Euclidean metrics or to the ideal hyperbolic metrics described by Charitos and Papadopoulos. Extending the results of our previous paper, we prove…
Consider a measurable space with a finite vector measure. This measure defines a mapping of the $\sigma$-field into a Euclidean space. According to Lyapunov's convexity theorem, the range of this mapping is compact and, if the measure is…
Since $n$-dimensional $\lambda$-hypersurfaces in the Euclidean space $\mathbb {R}^{n+1}$ are critical points of the weighted area functional for the weighted volume-preserving variations, in this paper, we study the rigidity properties of…
We study the compactness problem for moduli spaces of holomorphic supercurves which, being motivated by supergeometry, are perturbed such as to allow for transversality. We give an explicit construction of limiting objects for sequences of…
We show a geometric rigidity of isometric actions of non compact (semisimple) Lie groups on Lorentz manifolds. Namely, we show that the manifold has a warped product structure of a Lorentz manifold with constant curvature by a Riemannian…
We show numerically that the roughness and growth exponents of a wide range of rough surfaces, such as random deposition with relaxation (RDR), ballistic deposition (BD) and restricted solid-on-solid model (RSOS), are independent of the…
In \cite{BK02}, M. Bonk and B. Kleiner proved a rigidity theorem for expanding quasi-M\"obius group actions on Ahlfors $n$-regular metric spaces with topological dimension $n$. This led naturally to a rigidity result for quasi-convex…
Let $G\curvearrowright M$ be an isometric action of a Lie Group on a complete orientable Riemannian manifold. We disintegrate absolutely continuous measures with respect to the volume measure of $M$ along the principal orbits of…
The inclusion of rigid elements into elastic composites may lead to superior mechanical properties for the equivalent elastic continuum, such as, for instance, extreme auxeticity. To allow full exploitation of these properties, a tool for…
Given a parameter dependent fixed point equation $x = F(x,u)$, we derive an abstract compactness principle for the fixed point map $u \mapsto x^*(u)$ under the assumptions that (i) the fixed point equation can be solved by the contraction…
In this paper we show rigidity results for super-solutions to fully nonlinear elliptic conformally invariant equations on subdomains of the standard $n$-sphere $\mathbb S^n$ under suitable conditions along the boundary. We emphasize that…
Methods for measuring convexity defects of compacts in R^n abound. However, none of the those measures seems to take into account continuity. Continuity in convexity measure is essential for optimization, stability analysis, global…
It is proved some results about existence and non existence of unit normal sections of submanifolds of the Euclidean space and sphere which associated Gauss maps are harmonic. Some applications to CMC hypersurfaces of the sphere and…
The aim of this paper is to prove two results concerning the rigidity of complete, immersed, orientable, stable minimal hypersurfaces: we show that they are hyperplane in $\mathbb{R}^4$, while they do not exist in positively curved closed…