相关论文: Pseudoholomorphic Strips in Symplectisations I: As…

In this article, we extend the methods from arXiv:2011.06568, where the five dimensional analogue of the three dimensional finite energy foliations introduced by Hofer--Wysocki--Zehnder was identified, to the case where there the underlying…

This paper is motivated by the real symplectic isotopy problem : does there exists a nonsingular real pseudoholomorphic curve not isotopic in the projective plane to any real algebraic curve of the same degree? Here, we focus our study on…

Symplectic realization is a longstanding problem which can be traced back to Sophus Lie. In this paper, we present an explicit solution to this problem for an arbitrary holomorphic Poisson manifold. More precisely, for any holomorphic…

In any contact manifold of dimension $2n-1\geq 11$, we construct examples of closed legendrian submanifolds which are not diffeomorphic but whose lagrangian cylinders in the symplectization are hamiltonian isotopic.

This work is devoted to study of a class of elliptic singular perturbed systems and their singular limit to a phase segregating system. We prove existence and uniqueness and study the asymptotic behaviour with convergence to a limiting…

Recently, B.-Y. Chen and O. J. Garay studied pointwise slant submanifolds of almost Hermitian manifolds. By using the notion of pointwise slant submanifolds, we investigate the geometry of pointwise semi-slant submanifolds and their warped…

We give a necessary and sufficient condition for the existence of nondegenerate holomorphic mappings between pseudoellipsoidal real hypersurfaces, and provide an explicit parametrization for the collection of all such mappings (in the…

A symplectic rational cuspidal curve with positive self-intersection number admits a concave neighborhood, and thus a corresponding contact manifold on the boundary. In this article, we study symplectic fillings of such contact manifolds,…

We examine how symplectic cohomology may be used as an invariant on symplectic structures, and investigate the non-uniqueness of these structures on Liouville domains, a field which has seen much development in the past decade. Notably, we…

We continue the study of the recently-introduced C123-framework, for (simple) graph problems restricted to inputs specified by the forbidding of some finite set of subgraphs, to more general graph problems possibly involving multiedges and…

We study the deformations of a holomorphic symplectic manifold $M$, not necessarily compact, over a formal ring. We show (under some additional, but mild, assumptions on $M$) that the coarse deformation space exists and is smooth,…

We consider the Dirichlet Laplacian in a family of narrow unbounded domains. As the width of these domains goes to 0, we study the asymptotic behavior of the eigenvalues that lie below the essential spectrum and the asymptotic behavior of…

A venerable problem in combinatorics and geometry asks whether a given incidence relation may be realized by a configuration of points and lines. The classic version of this would ask for algebraic lines over some field or possibly real…

In this paper we examine the geometry of minimal surfaces of arithmetic hyperbolic 3-manifolds. In particular, we give bounds on the totally geodesic 2-systole, construct infinitely many incommensurable manifolds with the same initial…

In our companion work \cite{Stojnicl1RegPosasymldp} we revisited random under-determined linear systems with sparse solutions. The main emphasis was on the performance analysis of the $\ell_1$ heuristic in the so-called asymptotic regime,…

A symplectic form is called hyperbolic if its pull-back to the universal cover is a differential of a bounded one-form. The present paper is concerned with the properties and constructions of manifolds admitting hyperbolic symplectic forms.…

In this paper we give explicit, handle-by-handle constructions of concave symplectic fillings of all closed, oriented contact 3-manifolds. These constructions combine recent results of Giroux relating contact structures and open book…

Let E be a generic real submanifold of an almost complex manifold. The geometry of Bishop discs attached to E is studied in terms of the Levi form of E.

This paper presents two existence h-principles, the first for conformal symplectic structures on closed manifolds, and the second for leafwise conformal symplectic structures on foliated manifolds with non empty boundary. The latter…

This paper connects two different approaches to the analysis of Hamiltonian dynamics on non-compact energy hypersurfaces - $b$-symplectic geometry with its singular symplectic form and Floer techniques for tentacular Hamiltonians. More…