arXiv research

Classifies symmetries of non-flat 3-webs around a point.

Study circular foliations and shear-radius coordinates on hyperbolic cone surfaces.

For a knot $K\subset S^3$, its exterior $E(K) = S^3\backslashη(K)$ has a singular foliation by Seifert surfaces of $K$ derived from a circle-valued Morse function $f\colon E(K)\to S^1$. When $f$ is self-indexing and has no critical points of index 0 or 3, the regular levels that separate the index-1 and index-2 critica…

In this paper we extend our previous work on singularities of Monge-Ampère foliations to the case of pseudoconvex finite type domains. We are able to answer the questin of Burns on homogeneous polynomials whose logarithm satisfies the complex Monge-Ampère equation completely in dimension 2 . We are also able to general…

We study the problem of the existence and the holomorphicity of the Monge-Ampère foliation associated to a plurisubharmonic solutions of the complex homogeneous Monge-Ampère equation even at points of arbitrary degeneracy. We obtain good results for real analytic unbounded solutions. As a consequence we also provide a …

The relationships between braid ordering and the geometry of its closure is studied. We prove that if an essential closed surface $F$ in the complements of closed braid has relatively small genus with respect to the Dehornoy floor of the braid, $F$ is circular-foliated in a sense of Birman-Menasco's Braid foliation the…

This note provides some new perspectives and calculations regarding an interesting known family of minimal surfaces in $\mathbb{H}^2 \times \mathbb{R}$. The surfaces in this family are the catenoids, parabolic catenoids and tall rectangles. Each is foliated by either circles, horocycles or circular arcs in horizontal c…

The Euler class conjecture links geometric structures to integral points on the Thurston norm ball.

Study circular tractrices and pseudospheres in 3D space.

The paper defines circular orderability for quandles and explores their properties.

Paper studies geometric and combinatorial properties of circular snakes.

The study identifies surfaces with Maslovian normal bundles.

New hexagonal circular 3-webs with reducible curves classified.

Circular nets with spherical parameter lines have geometric properties related to Darboux cyclides and terminating Laplace sequences.

Paper proposes a method to improve circular coordinate representation for detecting changes in high-dimensional datasets.

The paper studies circular evolutes and involutes of framed curves in Euclidean space.

It was shown by Kaup that every origin-preserving automorphism of quasi-circular domains is a polynomial mapping. In this paper, we study how the weight of quasi-circular domains and the degree of such automorphisms are related. By using the Bergman mapping, we prove that every origin-preserving automorphism of normal …

CDFD analyzes circularity and directionality in weighted directed networks.

Classifies hexagonal circular 3-webs with cubic polar curves.

Study geometrically characterizes piecewise circular curves with decreasing curvature.

Curves become nearly circular over time without initial assumptions.

Study finds a limiting distribution for free path lengths on flat surfaces with circular obstacles.

We show that circular width is preserved under connected sum of knots for some cases.

The paper explores circular orderability in 3-manifold groups, related to the L-space conjecture.

Projected random forests improve circular data prediction with adaptive arc length and finite-sample coverage.

ANGLE tackles circular data regression, improving predictive performance.

Derives conformal parameters of curves using inscribed circular polygons.

Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by extending some standard probabilistic modelling tools to the circular domain. First w…

This article provides sufficient conditions for a closed hyperbolic 3-manifold $M$ with non zero first Betti number to fiber over the circle, and to find a fiber in $M$. Those conditions are formulated in terms of the behavior the circular characteristic in finite regular covers of $M$. We define the circular character…

A regular circle-valued Morse function on the knot complement C(K) = S^3\K is a function f from C(K) to S^1 which separates critical points and which behaves nicely in a neighborhood of the knot. Such a function induces a handle decomposition on the knot exterior E(K) = S^3\N (K), with the property that every regular l…

We study relations of some classes of $k$-convex, $k$-visible bodies in Euclidean spaces. We introduce and study \textrm{circular projections} in normed linear spaces and classes of bodies related with families of such maps, in particular, \textrm{$k$-circular convex} and \textrm{$k$-circular visible} ones. Investigati…

New conditions for circular orderability of direct products, linking to left-orderability of groups.

In this note we prove that any monohedral tiling of the closed circular unit disc with $k \leq 3$ topological discs as tiles has a $k$-fold rotational symmetry. This result yields the first nontrivial estimate about the minimum number of tiles in a monohedral tiling of the circular disc in which not all tiles contain t…

We show a non existence result for solutions of the prescribed mean curvature equation in the product manifold $\mathbb{H}^2 \times \R$, where $\mathbb{H}^2$ is the real hyperbolic plane. More precisely we prove a-priori estimates for graphs with constant mean curvature $h \in (0, 1/2]$ on circular annuli of $\mathbb{H…

Paper tackles circularity issues in machine learning predictions.

Method detects neural network equivalence via matrix ensembles and spectral analysis.

Elliptic bouquets defined for spin manifolds with circular actions.

Study stability and bifurcation of liquid interfaces in cylindrical supports.

Study convex embeddability in linear and circular orders, applying to knots.

We present a 2x2 Lax representation for discrete circular nets of constant negative Gauß curvature. It is tightly linked to the 4D consistency of the Lax representation of discrete K-nets (in asymptotic line parametrization). The description gives rise to Bäcklund transformations and an associated family. All the membe…

Numerous studies have been carried out to measure wind pressures around circular cylinders since the early 20th century due to its engineering significance. Consequently, a large amount of wind pressure data sets have accumulated, which presents an excellent opportunity for using machine learning (ML) techniques to tra…

This paper investigates the symplectic and contact topology associated to circular spherical divisors. We classify, up to toric equivalence, all concave circular spherical divisors $D$ that can be embedded symplectically into a closed symplectic 4-manifold and show they are all realized as symplectic log Calabi-Yau p…

A new machine learning framework called machine collaboration improves prediction accuracy.

We use technology from sutured manifold theory and the theory of Heegaard splittings to relate genus reducing crossing changes on knots in S^3 to twists on surfaces arising in circular Heegaard splittings for knot complements. In a separate paper, currently in preparation, we prove that these circular Heegaard splittin…

Motivated by well known results in low-dimensional topology, we introduce and study a topology on the set CO(G) of all left-invariant circular orders on a fixed countable and discrete group G. CO(G) contains as a closed subspace LO(G), the space of all left-invariant linear orders of G, as first topologized by Sikora. …

New algorithm for robust circular coordinates in recurrent time series data.

Proves Birkhoff-Poritsky conjecture for centrally-symmetric billiards.

Bayesian model predicts circular data with fast Gibbs sampling.