arXiv research

The paper introduces horizon saddle connections to study dilation surfaces.

We extend the construction of the Hennings TQFT for ribbon Hopf algebras to the case of ribbon quasi-Hopf algebras as defined by Drinfeld. Calculations proceed in a similar fashion to the ordinary Hopf algebra case, but also require the handling of the non-trivial coassociator in the triple tensor product of the algebr…

New 3D TQFTs derived from non-semisimple categories.

New invariants from symplectic fermions categorify link and manifold structures.

Using an extension of the Kontsevich integral to tangles in handlebodies similar to a construction given by Andersen, Mattes and Reshetikhin, we construct a functor $Z:\mathcal{B}\to \widehat{\mathbb{A}}$, where $\mathcal{B}$ is the category of bottom tangles in handlebodies and $\widehat{\mathbb{A}}$ is the degree-com…

Study of cuspidal edges on focal surfaces of regular surfaces.

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

Study on focal surfaces of lightcone framed surfaces in Lorentz-Minkowski 3-space.

Introduces hyperbolic generalized framed surfaces and their properties.

The paper studies special surfaces with a new type of support function.

Minimal Legendrian surfaces found in 5D sphere.

The paper studies knitted surfaces and surface-links, showing their isotopy and closure properties.

Classifies surfaces with constant Gaussian curvature in Euclidean 3-space.

We investigate surfaces with constant harmonic-mean curvature one (HMC-1 surfaces) in hyperbolic three-space. We allow them to have certain kinds of singularities, and discuss some global properties. As well as flat surfaces and surfaces with constant mean curvature one (CMC-1 surfaces), HMC-1 surfaces belong to a cert…

Unstable minimal surfaces in n-space link to hyperbolic products.

Researchers generalize Ribaucour-type surfaces with new mathematical representation.

Automorphisms of fine curve graphs match surface homeomorphisms for planar surfaces.

This paper connects Laguerre minimal surfaces to Weierstrass representations.

New surfaces in 4-ball constructed from knits, described by charts.

Study on singular points of translation surfaces under linearly dependent conditions.

Crochet patterns for minimal surfaces created using trigonometry.

New surfaces generalize Dini surfaces in 4D.

Here, we focus on focal surfaces of a tubular surface in Euclidean 3-space E^3: Firstly, we give the tubular surfaces with respect to Frenet and Darboux frames. Then, we define focal surfaces of these tubular surfaces. We get some results for these types of surfaces to become flat and we show that there is no minimal f…

New method classifies HCMU surfaces in 3D space forms as Weingarten surfaces.

Minimal surfaces are the only biharmonic in Sol3.

It is shown that any handle-irreducible summand of every stable-ribbon surface-link is a unique ribbon surface-link up to equivalences, so that every stable-ribbon surface-link is a ribbon surface-link. This is a generalization of a previously observed result for a stably trivial surface-link. Two observations are give…

This paper proves compactness of conformal Chern-minimal surfaces in Hermitian surfaces.

New surface class defined using osculating circles.

Study proves surfaces with constant curvature are simple shapes.

The article constructs Bolza-like surfaces for infinitely many genera and studies their properties.

The Enneper surface and helix surfaces are unique in their geometric properties.

Study on automorphisms of K3 and Enriques surfaces, proving entropy gaps and achirality.

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…

The paper connects least area surfaces to quasi-normal surfaces in 3-manifolds.

New concept of quasi-ribbon surface-links simplifies complex surface-links.

Study of timelike surfaces in Minkowski space with specific geometric properties.

The paper explores $K^α$-translators on parallel and canal surfaces in 3D space.

Researchers describe isometric deformations of T-hedra and T-surfaces.

The height function of various surfaces decomposes into finite sums of scaled and translated versions of itself.

The paper characterizes minimal surfaces and Lagrangian surfaces in complex projective space.

Defines spherical type surfaces via support function and classifies them.

Motivated by a number of recent investigations, we define and investigate the various properties of the ruled surfaces depend on three dimensional Lie groups with a bi-variant metric. We give useful results involving the characterizations of these ruled surfaces. Some special ruled surfaces such as normal surface, bino…

We study on a new kind of surface covered by translation and factorable (TF-type) surfaces in the three dimensional Euclidean space. We consider I and III Laplace-Beltrami operator surfaces of a TF-type surface. Then we obtain degrees and classes of algebraic surfaces of the surfaces using eliminate methods on software…

Defines Ribaucour-type surfaces and their properties.

The paper introduces groupoid racks for spatial surfaces.

General rotational surfaces as a source of examples of surfaces in the four-dimensional Euclidean space have been introduced by C. Moore. In this paper we consider the analogue of these surfaces in the Minkowski 4-space. On the base of our invariant theory of spacelike surfaces we study general rotational surfaces with…

The study classifies timelike meridian surfaces in Minkowski 4-space.

We develop a method to describe laws of random surfaces using surface holonomy.