相关论文: Bordered contact instantons and their Fredholm the…
This is the first of a series of papers in preparation in which we study the Hamiltonian perturbed contact instantons with Legendrian boundary condition and its applications. In this paper, we prove that the asymptotic charge of contact…
In Part I, we establish nonlinear ellipticity of the equation of contact instantons with Legendrian boundary condition on punctured Riemann surfaces by proving the a priori elliptic coercive estimates for the contact instantons with…
The purposes of the present paper are two-fold. Firstly we further develop the interplay between the contact Hamiltonian geometry and the geometric analysis of Hamiltonian-perturbed contact instantons with the Legendrian boundary condition,…
In the present article, we provide analytic foundation of the following nonlinear elliptic system, called the \emph{Hamiltonian-perturbed contact instanton equation}, $$ (du - X_H \otimes \gamma)^{\pi(0,1)} = 0, \quad d(e^{g_{H,…
In the paper we develop a general theory of solvability of linear inhomogeneous boundary-value problems for systems of first-order ordinary differential equations in spaces of smooth functions on a finite interval. This problems are set…
This paper ascertains the global behavior of the forward and backward branches of solutions provided by the Leray-Schauder continuation theorem for orientable $\mathcal{C}^1$ Fredholm maps, as developed by the authors in [54]. Under…
The present paper is a continuation of the study of the interplay between the contact Hamiltonian dynamics and the moduli theory of (perturbed) contact instantons and its applications initiated in [Oh21b, Oh22a]. In this paper we prove…
We develop the gluing theory of contact instantons in the context of open strings and in the context of closed strings \emph{with vanishing charge}, for example in the symplectization context. This is one of the key ingredients for the…
In [OW2,OW3], the authors studied the nonlinear elliptic system $$ \overline{\partial}^\pi w = 0, \, d(w^*\lambda \circ j) = 0 $$ without involving symplectization for each given contact triad $(Q,\lambda, J)$, and established the a priori…
For a given coorientable contact manifold $(M,\Xi)$ with contact distribution $\Xi$, we consider its contact forms $\lambda$ with $\ker \lambda = \Xi$, and the associated contact triads $(M,\lambda, J)$. For a generic choice of contact form…
A Fredholm integral equation of the second kind with the generalized Neumann kernel associated with the Riemann-Hilbert problem on unbounded multiply connected regions will be derived and studied in this paper. The derived integral equation…
We provide a thorough construction of a system of compatible determinant line bundles over spaces of Fredholm operators, fully verify that this system satisfies a number of important properties, and include explicit formulas for all…
In this paper, we prove Shelukhin's conjecture on the translated points on any closed contact manifold $(Q,\xi)$ which reads that for any choice of function $H = H(t,x)$ and contact form $\lambda$ the contactomorphism $\psi_H^1$ carries a…
The theory of frames normal for general connections on differentiable bundles is developed. Links with the existing theory of frames normal for covariant derivative operators (linear connections) in vector bundles are revealed. The…
Just as a symmetric surface with separating fixed locus halves into two oriented bordered surfaces, an arbitrary symmetric surface halves into two oriented symmetric half-surfaces, i.e. surfaces with crosscaps. Motivated in part by the…
We derive the large distance asymptotics of the Fredholm determinant of the so-called generalised sine kernel at the critical point. This kernel corresponds to a generalisation of the pure sine kernel arising in the theory of random…
This is the first of a series of papers in preparation on the Fukaya-type $A_\infty$ category generated by tame Legendrian submanifolds, called the Legendrian contact instanton Fukaya category (abbreviated as the Legendrian CI Fukaya…
In the present paper, we develop the Floer-style elliptic Morse theory for the Hamiltonian-perturbed contact action functional attached to the Legendrian links. Motivated by the present authors' construction [OY2] of the a perturbed action…
In the localization of 5-dimensional N = 1 super-Yang-Mills, contact-instantons arise as non-perturbative contributions. In this note, we revisit such configurations and discuss their generalizations. We propose for contact-instantons a…
In string field theory an infinitesimal background deformation is implemented as a canonical transformation whose hamiltonian function is defined by moduli spaces of punctured Riemann surfaces having one special puncture. We show that the…