Related papers: Smooth hyperbolicity cones are second-order cone r…

Let G be a second countable, locally compact group and let f be a continuous Herz-Schur multiplier on G. Our main result gives the existence of a (not necessarily uniformly bounded) strongly continuous representation on a Hilbert space,…

Let $p$ be an odd prime number, and $F$ a nonarchimedean local field of residual characteristic $p$. We classify the smooth, irreducible, admissible genuine mod-$p$ representations of the twofold metaplectic cover…

In this note we introduce the notion of a smooth structure on a conical pseudomanifold $M$ in terms of $C^\infty$-rings of smooth functions on $M$. For a finitely generated smooth structure $C^\infty (M)$ we introduce the notion of the Nash…

Let $G$ be a locally convex Lie group and $\pi:G \to \mathrm{U}(\mathcal{H})$ be a continuous unitary representation. $\pi$ is called smooth if the space of $\pi$-smooth vectors $\mathcal{H}^\infty\subset \mathcal{H}$ is dense. In this…

We perform a detailed analysis of the solvability of linear strain equations on hyperbolic surfaces. We prove that if the surface is a smooth noncharacteristic region, any first order infinitesimal isometry can be matched to an…

The deformation theory of hyperbolic and Euclidean cone-manifolds with all cone angles less then 2{\pi} plays an important role in many problems in low dimensional topology and in the geometrization of 3-manifolds. Furthermore, various old…

Let M be an almost Hermitian manifold of dimension greater or equal to 6. The following theorems are proved: Theorem 1. If M is of pointwise constant {\theta}-holomorphic sectional curvature for a number {\theta} in (0,{\pi}/2) then M is of…

An old open question in non-K\"ahler geometry predicts that any compact Hermitian manifold with constant holomorphic sectional curvature must be K\"ahler or Chern flat. The conjecture is known to be true in dimension $2$ due to the work by…

It is an open problem whether every continuous homomorphism between infinite-dimensional Lie groups is smooth. In this article, we show that every Hoelder continuous homomorphism is smooth.

We show that the cone over a fibered face of a compact fibered hyperbolic 3-manifold is dual to the cone generated by the homology classes of finitely many curves called minimal stable loops living in the associated veering triangulation.…

Let W -> X be a real smooth projective 3-fold fibred by rational curves. J. Koll\'ar proved that, if W(R) is orientable, then a connected component N of W(R) is essentially either a Seifert fibred manifold or a connected sum of lens spaces.…

We study spin structures on orbifolds. In particular, we show that if the singular set has codimension greater than 2, an orbifold is spin if and only if its smooth part is. On compact orbifolds, we show that any non-trivial twistor spinor…

We show that any compact surface of genus zero in Euclidean 3-space that satisfies a quasiconformal inequality between its principal curvatures is a round sphere. This solves an old open problem by H. Hopf, and gives a spherical version of…

We prove that an abstract (possibly infinite dimensional) complex irreducible representation of a discrete supersolvable group is monomial if and only if it has finite weight. We also prove a general result that implies converse of Schur's…

We prove that a 3-dimensional hyperbolic cusp with convex polyhedral boundary is uniquely determined by the metric induced on its boundary. Furthemore, any hyperbolic metric on the torus with cone singularities of positive curvature can be…

We show that smoothness implies norm-controlled inversion: the smoothness of an element $a$ in a Banach algebra with a one-parameter automorphism group is preserved under inversion, and the norm of the inverse $a^{-1}$ is controlled by the…

We prove that in every separable Banach space $X$ with a Schauder basis and a $C^k$-smooth norm it is possible to approximate, uniformly on bounded sets, every equivalent norm with a $C^k$-smooth one in a way that the approximation is…

We completely characterize isoperimetric regions in R^n with density e^h, where h is convex, smooth, and radially symmetric. In particular, balls around the origin constitute isoperimetric regions of any given volume, proving the Log-Convex…

In this paper I present an elementary construction to prove that any proper metric space can arise as the asymptotic cone of another proper metric space. Furthermore I answer a question of Drutu and Sapir concerning slow ultrafilters.

We extend the definition of conical representations for Riemannian symmetric spaces to a certain class of infinite-dimensional Riemannian symmetric spaces. Using an infinite-dimensional version of Weyl's Unitary Trick, there is a…