Related papers: Summability Condition and Rigidity for Finite Type…

A meromorphic quadratic differential on a compact Riemann surface defines a complex projective structure away from the poles via the Schwarzian equation. In this article we first prove the analogue of Thurston's Grafting Theorem for the…

Our work builds on known results for k-uniform hypergraphs including the existence of limits, a Regularity Lemma and a Removal Lemma. Our main tool here is a theory of measures on ultraproduct spaces which establishes a correspondence…

This is a survey article on the stable cohomotopy refinement of Seiberg-Witten invariants containing also new results, for example: - Stable cohomotopy groups describe path components of certain mapping spaces. - Relation of stable…

We introduce a natural stratification of the space of projective classes of measured laminations on a complete hyperbolic surface of finite area. We prove a rigidity result, namely, the group of self-homeomorphisms of the space of…

We adapt algorithms for resolving the singularities of complex algebraic varieties to prove that the natural map of homology theories from complex bordism to the bordism theory of complex derived orbifolds splits. In equivariant stable…

We consider the problem of satisfaction of boundary conditions when the generalized stress vector is given on the surfaces for elastic plates and shells. This problem was open also both for refined theories in the wide sense and…

We determine a strong form of the decomposition theorem for proper toric maps over finite fields.

The paper contains a review on recent progress in the deformational properties of smooth maps from compact surfaces $M$ to a one-dimensional manifold $P$. It covers description of homotopy types of stabilizers and orbits of a large class of…

We prove a rigidity property in non-Archimedean dynamics, reminiscent of Zdunik theorem in complex dynamics: every rational map whose equilibrium measure charges an interval in the Berkovich projective line is affine Bernoulli. Our proof is…

A classical result in complex geometry says that the automorphism group of a manifold of general type is discrete. It is more generally true that there are only finitely many surjective morphisms between two fixed projective manifolds of…

Using Dwork's theory, we prove a broad generalisation of his famous p-adic formal congruences theorem. This enables us to prove certain p-adic congruences for the generalized hypergeometric series with rational parameters; in particular,…

We extend to pairs classical results of R. Elkik on lifting of homomorphisms and algebraization. In particular, we establish algebraization of an affine rig-smooth formal variety with a rig-smooth closed subvariety. This solves…

Generalising an example by Girondo and Wolfart, we use finite group theory to construct Riemann surfaces admitting two or more regular dessins (i.e. orientably regular hypermaps) with automorphism groups of the same order, and in many cases…

We investigate extremal metrics at which various types of rigidity theorems involving scalar curvatures hold. The rigidity we discuss here is related to the rigidity theorems presented by Mario Listing in his previous preprint. More…

We establish a localized Bochner-type rigidity theorem for harmonic maps between Riemannian manifolds. Let $f : (M,g) \to (\overline{M},\overline{g})$ be a harmonic map from a compact manifold. Instead of assuming a global nonpositivity…

We study rational self-maps of $\mathbb{P}^{1}$ whose critical points all have finite forward orbit. Thurston's rigidity theorem states that outside a single well-understood family, there are finitely many such maps over $\mathbb{C}$ of…

The goal of this paper is to establish a general rigidity statement for abstract representations of elementary subgroups of Chevalley groups of rank at least 2 over a class of commutative rings that includes the localizations of 1-generated…

In this article we give an expository account of the holomorphic motion theorem based on work of M\`a\~n\'e-Sad-Sullivan, Bers-Royden, and Chirka. After proving this theorem, we show that tangent vectors to holomorphic motions have…

The paper studies the deformation theory of a holomorphic surjective map from a normal compact complex space to a compact Kaehler manifold and describes the component of the space of holomorphic maps, generalizing results in the projective…

In this paper we aim to present two general results regarding, on one hand, the openness stability of set-valued maps and, on the other hand, the metric regularity behavior of the implicit multifunction related to a generalized variational…