arXiv research

Proves effective slope gaps for lattice surfaces.

Periodic surfaces have a limited number of bending modes, equal to their membrane modes.

We prove an effective version of a theorem relating curve complex distance to electric distance in hyperbolic 3-manifolds, up to errors that are polynomial in the complexity of the underlying surface. We use this to give an effective proof of a result regarding maps between curve complexes of surfaces induced by finite…

The paper classifies surfaces with pseudo-effective tangent bundles.

In this work, we are concerned with the spherical quasiconformal parameterization of genus-0 closed surfaces. Given a genus-0 closed triangulated surface and an arbitrary user-defined quasiconformal distortion, we propose a fast algorithm for computing a spherical parameterization of the surface that satisfies the pres…

Enhanced bikei modules distinguish unoriented and non-orientable surface-links.

This paper presents a method to obtain geometric registrations between high-genus ($g\geq 1$) surfaces. Surface registration between simple surfaces, such as simply-connected open surfaces, has been well studied. However, very few works have been carried out for the registration of high-genus surfaces. The high-genus t…

We classify the transitive, effective, holomorphic actions of connected complex Lie groups on complex surfaces.

We address the problem of surface inpainting, which aims to fill in holes or missing regions on a Riemann surface based on its surface geometry. In practical situation, surfaces obtained from range scanners often have holes where the 3D models are incomplete. In order to analyze the 3D shapes effectively, restoring the…

Characterizes solutions to Z-critical equations on surfaces using effective conditions.

A study on the relation between the smooth structure of a symplectic homotopy K3 surface and its symplectic symmetries is initiated. A measurement of exoticness of a symplectic homotopy K3 surface is introduced, and the influence of an effective action of a K3 group via symplectic symmetries is investigated. It is show…

Estimates surface count with prescribed foliations.

In this paper, we are concerned with the problem of creating flattening maps of simply-connected open surfaces in $\mathbb{R}^3$. Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing density-equalizing flattening maps with any prescribed density distribution. By var…

New solutions found for bending of flat surfaces and origami structures.

Mapping class group dynamics tracked through Teichmüller space.

Study of curves in rational surfaces using multisections and torus actions.

Surface parameterizations and registrations are important in computer graphics and imaging, where 1-1 correspondences between meshes are computed. In practice, surface maps are usually represented and stored as 3D coordinates each vertex is mapped to, which often requires lots of storage memory. This causes inconvenien…

We describe the positive cone and the pseudo-effective cone of a non-Kählerian surface. We use these results for two types of applications: - Describe the set $σ(X)$ of possible total Ricci scalars associated with Gauduchon metrics of fixed volume 1 on a fixed non-Kähhlerian surface, and decide whether the assignment $…

The study of stable minimal surfaces in Riemannian $3$-manifolds $(M, g)$ with non-negative scalar curvature has a rich history. In this paper, we prove rigidity of such surfaces when $(M, g)$ is asymptotically flat and has horizon boundary. As a consequence, we obtain an effective version of the positive mass theorem …

Estimates geodesic count on hyperbolic surfaces.

Formula proves Euler characteristic of singularized surfaces.

Study compares different complexity criteria for free boundary minimal surfaces.

New concept of effective isometries for compliant shells.

Paper estimates upper bound of analytic torsion under Arakelov metric.

Invariants for surfaces up to rigid transformations, with a comeagre subset retrieval algorithm.

Ray marching method visualizes flat surfaces efficiently.

The paper characterizes isomorphic covers of surfaces and applies it to distinguish representations.

The study finds effective lower bounds for spectra of random surfaces and bundles.

We refine Osserman's argument on the exceptional values of the Gauss map of algebraic minimal surfaces. This gives an effective estimate for the number of exceptional values and the totally ramified value number for a wider class of complete minimal surfaces that includes algebraic minimal surfaces. It also provides a …

The main goal of this paper is to reveal the geometric meaning of the maximal number of exceptional values of Gauss maps for several classes of immersed surfaces in space forms, for example, complete minimal surfaces in the Euclidean three-space, weakly complete improper affine spheres in the affine three-space and wea…

A stationary rotating surface is a compact surface in Euclidean space whose mean curvature $H$ at each point $x$ satisfies $2H(x)=a r^2+b$, where $r$ is the distance from $x$ to a fixed straight-line $L$, and $a$ and $b$ are constants. These surfaces are solutions of a variational problem that describes the shape of a …

This work relates the framework of model-based clustering for spatial functional data where the data are surfaces. We first introduce a Bayesian spatial spline regression model with mixed-effects (BSSR) for modeling spatial function data. The BSSR model is based on Nodal basis functions for spatial regression and accom…

Study finds how periodic surfaces can bend without stretching.

Study shows how many crossings arise in curves on surfaces.

Study null energy condition impacts on special hypersurfaces in static spacetimes.

Study of red blood cells using elastic surface theory.

In this paper, we formulate a construction of ideal coset invariants for surface-links in $4$-space using invariants for knots and links in $3$-space. We apply the construction to the Kauffman bracket polynomial invariant and obtain an invariant for surface-links called the Kauffman bracket ideal coset invariant of sur…

In this paper, we prove effective estimates for the number of exceptional values and the totally ramified value number for the Gauss map of pseudo-algebraic minimal surfaces in Euclidean four-space and give a kind of unicity theorem.

Study shows convergence of cscK surfaces in Hilbert scheme.

Model captures SPX and VIX volatility surfaces and skew-stickiness ratio.

Study of quantum aspects of generalized Gross-Neveu models, focusing on sigma models.

We study the change of moduli spaces of Gieseker-semistable torsion free rank-$2$ sheaves on algebraic surfaces as we vary the polarizations. When the surfaces are rational with an effective anti-canonical divisor, the moduli spaces are linked by a series of flips (blowups and blowdowns). Using these results, we comput…

New approach to extremal hyperbolic surfaces using NEC groups.

The paper finds hyperbolic metrics on surfaces with boundary using combinatorial curvature flows.

The paper introduces combinatorial Calabi flows to find hyperbolic metrics on surfaces with boundary.

We provide analogues for non-orientable surfaces with or without boundary or punctures of several basic theorems in the setting of the Thurston theory of surfaces which were developed so far only in the case of orientable surfaces. Namely, we provide natural analogues for non-orientable surfaces of the Fenchel-Nielsen …

New tools reveal simple structure in complex hyperparameter loss surfaces near optima.

In this thesis we consider a way to construct a rich family of compact Riemann Surfaces in a combinatorial way. Given a 3-regualr graph with orientation, we construct a finite-area hyperbolic Riemann surface by gluing triangles according to the combinatorics of the graph. We then compactify this surface by adding finit…