arXiv research

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

Study on complexity of systolic geodesics on Bolza surface.

Extremal length systole is maximized at the Bolza surface.

New algorithms compute points on generalized Bolza surfaces.

We give a detailed description of the arithmetic Fuchsian group of the Bolza surface and the associated quaternion order. This description enables us to show that the corresponding principal congruence covers satisfy the bound sys(X) > 4/3 log g(X) on the systole, where g is the genus. We also exhibit the Bolza group a…

We study Deraux's non arithmetic orbifold ball quotient surfaces obtained as birational transformations of a quotient $X$ of a particular Abelian surface $A$. Using the fact that $A$ is the Jacobian of the Bolza genus $2$ curve, we identify $X$ as the weighted projective plane $\mathbb{P}(1,3,8)$. We compute the equati…

In this paper, we settle in the affirmative the Jakobson-Levitin-Nadirashvili-Nigam-Polterovich conjecture, stating that a certain singular metric on the Bolza surface, with area normalized, should maximize the first eigenvalue of the Laplacian.

New formula and algorithm for computing distances on complex Riemann surfaces.

Algorithm morphs graphs on hyperbolic surfaces.

The paper proves unique geodesics on hyperbolic surfaces and finds lower bounds.

We prove an optimal systolic inequality for CAT(0) metrics on a genus~2 surface. We use a Voronoi cell technique, introduced by C.~Bavard in the hyperbolic context. The equality is saturated by a flat singular metric in the conformal class defined by the smooth completion of the curve y^2=x^5-x. Thus, among all CAT(0) …

The paper derives upper bounds on eigenvalues of Laplace-Beltrami operator on hyperbolic surfaces.

We borrow a classical construction from the study of rational billiards in dynamical systems known as the "unfolding construction" and show that it can be used to study the automorphism group of a Platonic surface. More precisely, the monodromy group, or deck group in this case, associated to the cover of a regular pol…

Exact diameter found for some Riemann surfaces.

We construct infinite families of closed hyperbolic surfaces that are local maxima for the systole function on their respective moduli spaces. The systole takes values along a linearly divergent sequence $(L_n)_{n\geq 1}$ at these local maxima. The only surface corresponding to $L_1\approx 3.057$ is the Bolza surface i…

The paper develops mathematical models for neural networks using non-compact symmetric spaces.

Geometrically, spherical 3-manifolds emerge from flat SU(2)-bundles over hyperbolic surfaces.

Method constrains spectral gaps of hyperbolic spin surfaces using identities and semidefinite programming.

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.

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.

Study proves surfaces with constant curvature are simple shapes.

New surface class defined using osculating circles.

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.