Related papers: Residual Cauchy-type formula on Riemann surfaces

For tri-diagonal matrices arising in the simplified Jaynes--Cummings model, we give an asymptotics of the eigenvalues, prove a trace formula and show that the Spectral Riemann Surface is irreducible.

We give upper bounds of the numbers of holomorphic sections of Veech holomorphic families of Riemann surfaces. The numbers depend only on the topological types of base Riemann surfaces and fibers. We also show a relation between types of…

Author of this article created for the first time the method for finding solutions of the Minkowski problem for closed surfaces in Riemannian space.

We give an estimate of type sup $\times$ inf on Riemannian manifold of dimension 4 for a Yamabe type equation.

Explicit formulas for the Gauss decomposition of elliptic Cauchy type matrices are derived in a very simple way. The elliptic Cauchy identity is an immediate corollary.

We show well-posedness for the parabolic Anderson model on $2$-dimensional closed Riemannian manifolds. To this end we extend the notion of regularity structures to curved space, and explicitly construct the minimal structure required for…

By modifying Cole's example, we construct explicit Riemann surfaces with large bounds on corona solutions in an elementary way.

We prove an analogue of the Cauchy integral theorem for hyperholomorphic functions given in three-dimensional domains with non piece-smooth boundaries and taking values in an arbitrary finite-dimensional commutative associative Banach…

We consider in this paper an area functional defined on submanifolds of fixed degree immersed into a graded manifold equipped with a Riemannian metric. Since the expression of this area depends on the degree, not all variations are…

We show sufficient and necessary conditions, in terms of some partial differential equations with variable coefficients, for a quaternionic function to admit a continuous derivative in a open set in the sense of C. Schwartz.

We generalize Warnaar's elliptic extension of a Macdonald multiparameter summation formula to Riemann surfaces of arbitrary genus.

We obtain a sub-Riemannian version of the classical Gauss-Bonnet theorem. We consider subsurfaces of a three dimensional contact sub-Riemannian manifolds, and using a family of taming Riemannian metric, we obtain a pure sub-Riemannian…

We present explicit expressions for the Maurer-Cartan forms of the superdiffeomorphism group associated to a super Riemann surface. As an application to superconformal field theory, we use these forms to evaluate the effective action for…

In this paper, we prove new rigidity results related to some generalised Ricci-Hessian equation on Riemannian manifolds.

Here we will consider examples of conformally flat manifolds that are conformally equivalent to open subsets of the n-dimensional sphere. For such manifolds we shall introduce a Cauchy kernel and Cauchy integral formula for sections tasking…

Let S be a surface obtained from a plane polygon by identifying infinitely many pairs of segments along its boundary. A condition is given under which the complex structure in the interior of the polygon extends uniquely across the quotient…

We devise some differential forms after Chern to compute a family of formulas for comparing total mean curvatures of nested hypersurfaces in Riemannian manifolds. This yields a quicker proof of a recent result of the author with Joel…

In this paper, we provide formulas for the sum of residues of type Camacho-Sad of a holomorphic foliation with respect to an invariant analytic subvariety. As application, in context of projective foliations, we obtain a formula that…

The purpose of this paper is to point out a relation between the canonical sheaf and the intersection complex of a singular algebraic variety. We focus on the hypersurface case. Let $M$ be a complex manifold, $X\subset M$ a singular…

Any open Riemann surface $R_0$ of finite genus $g$ can be conformally embedded into a closed Riemann surface of the same genus, that is, $R_0$ is realized as a subdomain of a closed Riemann surface of genus $g$. We are concerned with the…