arXiv research

Transforms curves and surfaces for efficient geometric analysis.

Complex analysis aids in studying minimal surfaces.

Study axisymmetric surfaces in Euclidean space for energy minimization.

Sharp inequalities and extremals on compact Riemann surfaces with boundary.

Constructs surfaces with conical singularities using variational methods.

We study Tikhonov regularization for solving ill--posed operator equations where the solutions are functions defined on surfaces. One contribution of this paper is an error analysis of Tikhonov regularization which takes into account perturbations of the surfaces, in particular when the surfaces are approximated by spl…

New analysis of crushing surfaces of positive genus impacts triangulation complexity.

This is a guided tour through some selected topics in geometric analysis. We have chosen to illustrate many of the basic ideas as they apply to the theory of minimal surfaces. This is, in part, because minimal surfaces is, if not the oldest, then certainly one of the oldest areas of geometric analysis dating back to Eu…

This note provides a new proof of the real analyticity of the Liouville map.

The paper constructs surfaces with prescribed mean curvature in a specific space.

Analyzes magnetic Laplacian on hyperbolic surfaces, highlighting key quantum phenomena.

Study on ion travel time on curved surfaces.

Paper connects surface shape analysis and unbalanced optimal transport.

No nontrivial automorphisms for cubic surfaces moduli space.

Lectures on surface evolution through singularities.

We study a class of fourth-order geometric problems modelling Willmore surfaces, conformally constrained Willmore surfaces, isoperimetrically constrained Willmore surfaces, bi-harmonic surfaces in the sense of Chen, among others. We prove several local energy estimates and derive a global gap lemma.

Two infinite sequences of minimal surfaces in space are constructed using symmetry analysis. In particular, explicit formulas are obtained for the self-intersecting minimal surface that fills the trefoil knot.

Study rotational surfaces with prescribed Gauss curvature in 3D space.

New method for surface analysis using restricted deformation bases.

The paper studies timelike minimal surfaces in De Sitter space using complex analysis.

Study uses sentiment analysis to predict implied volatility surface, improving prediction accuracy.

Study of 17 surface behaviors and singularities for elliptic Weingarten equations.

Survey on geometric properties of special minimal surfaces.

The paper classifies helicoidal surfaces with specific curvature functions.

Introduces hyperbolic generalized framed surfaces and their properties.

Study harmonic surfaces in 3D space, proving superposition principle.

SRNF framework extends surface distance to Lipschitz surfaces.

We show that surface groups are flexibly stable in permutations. This is the first non-trivial example of a non-amenable flexibly stable group. Our method is purely geometric and relies on an analysis of branched covers of hyperbolic surfaces. Along the way we establish a quantitative variant of the LERF property for s…

New method glues Scherk surfaces into minimal surfaces, limiting possible outcomes.

Isogeometric analysis is a recently developed computational approach that integrates finite element analysis directly into design described by non-uniform rational B-splines (NURBS). In this paper we show that price surfaces that occur in option pricing can be easily described by NURBS surfaces. For a class of stochast…

A new method simulates implied volatility surfaces for multiple assets.

In this paper, we make some remarks on José Espinar's paper "Finite index operators on surfaces" [\texttt{arXiv:0911.3767}, to appear in Journal of Geometric Analysis (2011)].

Unified treatment of spacelike and timelike minimal surfaces via Liouville equation.

Simply connected surfaces with large constant mean curvature and free boundaries concentrate at critical points of the boundary's mean curvature.

Proves quantitative Alexandrov theorem for capillary surfaces.

Normal surface theory is a central tool in algorithmic three-dimensional topology, and the enumeration of vertex normal surfaces is the computational bottleneck in many important algorithms. However, it is not well understood how the number of such surfaces grows in relation to the size of the underlying triangulation.…

The paper examines stable CMC hypersurfaces with boundaries on parallel hyperplanes.

A new complex space resolves projective structures on surfaces.

Introduces minimal surfaces to undergraduates.

Refines geometric center of mass analysis for Einstein field equations.

Timelike Thomsen surfaces are timelike minimal surfaces that are also affine minimal. In this paper, we make use of both the Lorentz conformal coordinates and the null coordinates, and their respective representation theorems of timelike minimal surfaces, to obtain a complete global classification of these surfaces and…

Flat fully augmented links with homeomorphic complements are equivalent.

Dynamic functional time-series methods improve forecast accuracy for foreign exchange implied volatility surfaces.

We consider a surface $M$ immersed in $\mathbb{R}^3$ with induced metric $g=ψδ_2$ where $δ_2$ is the two dimensional Euclidean metric. We then construct a system of partial differential equations that constrain $M$ to lift to a minimal surface via the Weierstrauss-Enneper representation demanding the metric is of the a…

Harmonic maps from Riemann surfaces arise from a conformally invariant variational problem. Therefore, on one hand, they are intimately connected with moduli spaces of Riemann surfaces, and on the other hand, because the conformal group is noncompact, constitute a prototype for the formation of singularities, the so-ca…

In this article we propose a generalisation of the recent work of Gatheral and Jacquier on explicit arbitrage-free parameterisations of implied volatility surfaces. We also discuss extensively the notion of arbitrage freeness and Roger Lee's moment formula using the recent analysis by Roper. We further exhibit an arbit…

Formula proves almost monotonicity for H-minimal surfaces in Heisenberg group.

Checkerboard surfaces in alternating link complements are used frequently to determine information about the link. However, when many crossings are added to a single twist region of a link diagram, the geometry of the link complement stabilizes (approaches a geometric limit), but a corresponding checkerboard surface in…