Related papers: Summing Over World-Sheet Boundaries
We extend the lightcone worldsheet lattice approach to string theory, proposed in 1977 by Giles and me, to allow for coincident D-branes. We find a convenient lattice representation of Dirichlet boundary conditions, which the open string…
This paper presents an overview of recent developments in the analysis of shapes such as curves and surfaces through Riemannian metrics. We show that several constructions of metrics on spaces of submanifolds can be unified through the…
We discuss some relations of moduli of sheaves on rational surfaces by using universal extensions. These are a generalization of Maruyama's method to construct Uhlenbeck compactification of moduli of vector bundles.
In this paper we continue the study started in part I (posted). We consider a planar, bounded, $m$-connected region $\Omega$, and let $\bord\Omega$ be its boundary. Let $\mathcal{T}$ be a cellular decomposition of $\Omega\cup\bord\Omega$,…
These notes on Riemannian geometry use the bases bundle and frame bundle, as in Geometry of Manifolds, to express the geometric structures. It has more problems and omits the background material. It starts with the definition of Riemannian…
Miura surfaces are the solutions of a constrained nonlinear elliptic system of equations. This system is derived by homogenization from the Miura fold, which is a type of origami fold with multiple applications in engineering. A previous…
We study the problem of imposing Dirichlet-like boundary conditions along a static spatial curve, in a planar Noncommutative Quantum Field Theory model. After constructing interaction terms that impose the boundary conditions, we discuss…
In this article we address a number of features of the moduli space of spherical metrics on connected, compact, orientable surfaces with conical singularities of assigned angles, such as its non-emptiness and connectedness. We also consider…
Let ${\mathcal M}_g$ be the moduli space of compact connected Riemann surfaces of genus $g\geq 2$ and let $\widehat{{\mathcal M}_g}$ be its Deligne-Mumford compactification, which is stratified by the topological type of the stable Riemann…
We introduce a simple procedure to integrate differential forms with arbitrary holomorphic poles on Riemann surfaces. It gives rise to an intrinsic regularization of such singular integrals in terms of the underlying conformal geometry.…
An explicit canonical construction of monopole connections on non trivial U(1) bundles over Riemann surfaces of any genus is given. The class of monopole solutions depend on the conformal class of the given Riemann surface and a set of…
We construct supersymmetric gauge theories on some curved manifolds with boundaries. Our examples include a part of three-sphere and a part of two-sphere. We concentrate on Dirichlet boundary conditions. For these theories on the manifolds…
In this paper we consider the inverse problem of determining on a compact Riemannian manifold the electric potential and the absorption coefficient in the wave equation with Dirichlet data from measured Neumann boundary observations. This…
Upper bounds for the eigenvalues of the Laplace-Beltrami operator on a hypersurface bounding a domain in some ambient Riemannian manifold are given in terms of the isoperimetric ratio of the domain. These results are applied to the…
We consider general shape optimization problems governed by Dirichlet boundary value problems. The proposed approach may be extended to other boundary conditions as well. It is based on a recent representation result for implicitly defined…
We show that certain structures and constructions of the Whitham theory, an essential part of the perturbation theory of soliton equations, can be instrumental in understanding the geometry of the moduli spaces of Riemann surfaces with…
The magnetic Dirichlet-to-Neumann map encodes the voltage-to-current measurements under the influence of a magnetic field. In the case of surfaces, we provide precise spectral asymptotics expansion (up to arbitrary polynomial power) for the…
One of the basic geometric objects in conformal field theory (CFT) is the the moduli space of Riemann surfaces whose $n$ boundaries are ''rigged'' with analytic parametrizations. The fundamental operation is the sewing of such surfaces…
This is a survey paper dealing with moduli aspects of curves over finite fields. It discusses counting points of moduli spaces, relations with modular forms and stratifications on moduli spaces.
The dependence of the Virasoro-$N$-point function on the moduli of the Riemann surface is investigated. We propose an algebraic geometric approach that applies to any hyperelliptic Riemann surface.