Related papers: Measured lamination spaces for surface pairs
This article presents a novel mathematical formalism for advanced manifold--metric pairs, enhancing the frameworks of geometry and topology. We construct various D-dimensional manifolds and their associated metric spaces using functional…
This paper gives an explicit formula for the Ehrhart quasi-polynomial of certain 2-dimensional polyhedra in terms of invariants of surface quotient singularities. Also, a formula for the dimension of the space of quasi-homogeneous…
The space of measured laminations $\mathcal{ML}(\Sigma)$ associated to a topological surface $\Sigma$ of genus $g$ with $n$ punctures is an integral piecewise linear manifold of real dimension $6g-6+2n$. There is also a natural symplectic…
To understand the structure of an algebraic variety we often embed it in various projective spaces. This develops the notion of projective geometry which has been an invaluable tool in algebraic geometry. We develop a perfectoid analog of…
A series of ceramic artworks are presented, inspired by the author's research connecting theoretical physics to the beautiful theory of Riemann surfaces. More specifically the research is related to the classification of curves on the…
In this paper, we investigate some properties of planar harmonic mappings. First, we generalize the main results in \cite{CPW3} and \cite{HT}, and then discuss the relationship between area integral means and harmonic Hardy spaces or…
From descent theory to higher geometry, the idea of gluing has been embedded in many elegant and powerful techniques, proving instrumental for the solution of many problems. In this paper, we introduce a framework that allows to link…
The algebraic translational surface is a typical modeling surface in computer aided design and architecture industry. In this paper, we give a necessary and sufficient condition for that algebraic surface having a standard parametric…
We prove genuinely multilinear weighted estimates for singular integrals in product spaces. The estimates complete the qualitative weighted theory in this setting. Such estimates were previously known only in the one-parameter situation.…
We describe a construction of ordered algebraic structures (ordered abelian semigroups, ordered commutative semirings, etc.) and describe applications to codimension-1 laminations. For a suitable ordered semi- algebraic structure $\mathbb…
We construct moduli spaces of framed logarithmic connections and also moduli spaces of framed parabolic connections. It is shown that these moduli spaces possess a natural algebraic symplectic structure. We also give an upper bound of the…
We prove some sharp extremal distance results for functions in weighted Bergman spaces on the upper halfplane.We also prove such results in the context of bounded strictly pseudoconvex domains with smooth boundary
A perturbative technique, the low-temperature expansion, is developed for matrix models of random surfaces. It can be applied to models with arbitrary target spaces, including ones with c>1. As a simple illustration, the series is worked…
Given a description of the stacking statistics of layered close-packed structures in the form of a hidden Markov model, we develop analytical expressions for the pairwise correlation functions between the layers. These may be calculated…
In this paper, we introduce, for a separable Banach spacea new notion of besselian paires and of besselian Schauder frames for which we prove for some fundamental results.
The article surveys published and not yet published results about moduli spaces of algebraic surfaces.
The aim of this paper is to extend classic results of the theory of CMC surfaces in the product spaces to the class of immersed surfaces in $\mathbb{M}^2(\kappa)\times\mathbb{R}$ whose mean curvature is given as a $C^1$ function depending…
We give an algorithm to compute the periods of smooth projective hypersurfaces of any dimension. This is an improvement over existing algorithms which could only compute the periods of plane curves. Our algorithm reduces the evaluation of…
We extend the notion of regularized integrals introduced by Li-Zhou that aims to assign finite values to divergent integrals on configuration spaces of Riemann surfaces. We then give cohomological formulations for the extended notion using…
We develop an algorithm computing the transcendental lattice and the Mordell--Weil group of an extremal elliptic surface. As an example, we compute the lattices of four exponentially large series of surfaces