Related papers: An extension theorem in symplectic geometry

We show, in this note, that on any symplectic supermanifold, even or odd, there exist an infinite dimensional affine space of symmetric connections, compatible to the symplectic form.

The Darboux theorem in symplectic geometry implies that any two points in a connected symplectic manifold have neighbourhoods symplectomorphic to each other. The impossibility of such a theorem in the more general multisymplectic framework…

The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…

It is shown that a valuation of residue characteristic different from $2$ and $3$ on a field $E$ has at most one extension to the function field of an elliptic curve over $E$, for which the residue field extension is transcendental but not…

In this paper we start with the applications of polyfold theory to symplectic field theory.

We prove the validity of maximum principles for a class of fully nonlinear operators on unbounded subdomains $\Omega \subset \mathbb R^n$ of cylindrical type. The main structural assumption is the uniform ellipticity of the operator along…

We study extensions of Sem\"enov arithmetic, the first-order theory of the structure $(\mathbb{N}, +, 2^x)$. It is well-knonw that this theory becomes undecidable when extended with regular predicates over tuples of number strings, such as…

A fundamental result of Springer says that a quadratic form over a field of characteristic not 2 is isotropic if it is so after an odd degree extension. In this paper we generalize Springer's theorem as follows. Let R be a an arbitrary…

In this paper we build up a criteria for fractional Orlicz-Sobolev extension and imbedding domains on Ahlfors $n$-regular domains.

Brehm's extension theorem states that a non-expansive map on a finite subset of a Euclidean space can be extended to a piecewise-linear map on the entire space. In this note, it is verified that the proof of the theorem is constructive…

In this work we bring together tools and ideology from two different fields, Symplectic Geometry and Asymptotic Geometric Analysis, to arrive at some new results. Our main result is a dimension-independent bound for the symplectic capacity…

We give a full characterization of embeddings of the unit circle that admit a Sobolev homeomorphic extension to the unit disk. As a direct corollary, we establish that for quasiconvex target domains $\mathbb Y$, any homeomorphism $\varphi…

We extend Hardy's uncertainty principle for a square integrable function and its Fourier transform to the multidimensional case using a symplectic diagonalization. We use this extension to show that Hardy's uncertainty principle is…

In a neighborhood of isolated point of a domain of a metric space, a behavior of generalized quasiconformal mappings is studied. It is proved that, mappings mentioned above have continuous extension to the domain at some additional…

In this paper we obtain new obstructions to symplectic embeddings of the four-dimensional polydisk $P(a,1)$ into the ball $B(c)$ for $2\leq a<\frac{\sqrt{7}-1} {\sqrt{7}-2} \approx 2.549$, extending work done by Hind-Lisi and Hutchings.…

We study problems related to continuous boundary extension of mappings of Orlicz-Sobolev classes in terms of prime ends. The results we obtain concern the case when the mappings are open, discrete, but not closed (not preserving the…

We use spectral theory and algebraic geometry to establish a higher-degree analogue of a Szemer\'edi--Trotter-type theorem over finite fields, with an application to polynomial expansion.

The notion of geometric version of an infinitely divisible law is introduced. Concepts parallel to attraction and partial attraction are developed and studied in the setup of geometric summing of random variables.

For some class of mappings, there are investigated problems connected with a possibility of continuous extension to a boundary on Riemannian manifolds. In particular, for so-called ring mappings, there is proved a result related to…

We present a survey of some results and questions related to the notion of scalar curvature in the setting of symplectic supermanifolds.