arXiv research

Study shows non-compact convex hulls in certain metric spaces.

Sharp Poincaré inequality proved for specific metric spaces.

The paper derives explicit geodesic equations for a specific type of group structure.

Any two compact, complete, one-dimensional geodesic spaces with identical marked length spectrum have isometric $π_1$-hull. The present version contains errors, notably in Lemmas 2.2 and 2.3 (path cancellations can be more complicated), which then propagate through the paper. The main result is correct as stated, and a…

We consider non-elementary representations of two generator free groups in $PSL(2,\mathbb{C})$, not necessarily discrete or free, $G = < A, B >$. A word in $A$ and $B$, $W(A,B)$, is a palindrome if it reads the same forwards and backwards. A word in a free group is {\sl primitive} if it is part of a minimal generating …

For every finite collection of curves on a surface, we define an associated (semi-)norm on the first homology group of the surface. The unit ball of the dual norm is the convex hull of its integer points. We give an interpretation of these points in terms of certain coorientations of the original collection of curves. …

We present a nonstandard hull construction for locally uniform groups in a spirit similar to Luxembourg's construction of the nonstandard hull of a uniform space. Our nonstandard hull is a local group rather than a global group. We investigate how this construction varies as one changes the family of pseudometrics used…

This paper defines maximal measurable cocycles for surface groups into Hermitian Lie groups and studies their algebraic hulls.

Various results based on some convexity assumptions (involving the exponential map along with affine maps, geodesics and convex hulls) have been recently established on Hadamard manifolds. In this paper we prove that these conditions are mutually equivalent and they hold if and only if the Hadamard manifold is isometri…

The paper characterizes sets with infinite hyperbolic convex hull volume.

Let $S$ be a compact, connected, oriented surface, possibly with boundary, of negative Euler characteristic. In this article we extend Lindenstrauss-Mirzakhani's and Hamenstädt's classification of locally finite mapping class group invariant ergodic measures on the space of measured laminations $\mathcal{M}\mathcal{L}(…

The n-th hull of a union of curves in R^3 is the set of points with the property: Any plane passing through the point intersects the curves at least 2n times. The hull number u(L) of a link L is defined as the minimum number of non-empty hulls a representative of L can have. We show that the hull numbers of torus links…

The main result of this paper is a characterization of the minimal surface hull of a compact set $K$ in $\mathbb R^3$ by sequences of conformal minimal discs whose boundaries converge to $K$ in the measure theoretic sense, and also by $2$-dimensional minimal currents which are limits of Green currents supported by conf…

Designing and modifying complex hull forms for optimal vessel performances have been a major challenge for naval architects. In the present study, Principal Component Analysis (PCA) is introduced to compress the geometric representation of a group of existing vessels, and the resulting principal scores are manipulated …

Fixed points found in Teichmüller space via anti-de Sitter geometry.

Develops harmonic metrics for Hull-Strominger system stability.

Study analyzes correlation structure in two-factor Hull-White model for XVA calculations.

Deep learning models generalize by extending decision boundaries outside the convex hull of training data.

Let $\mathcal{W}^{n}$ be the class of $C^{\infty }$ complete simply connected $n-$dimensional manifolds without conjugate points. The hyperbolic space as well as Euclidean space are good examples of such manifolds. Let $$ and let $A$ be a subset of $W$. This article aims at characterization and bu…

The paper transforms a convex hull into a concave surface around a point cloud.

The integer hull of a polyhedron is the convex hull of the integer points contained in it. We show that the vertices of the integer hulls of a rational family of polyhedra of size O(n) have quasipolynomial coordinates. As a corollary, we show that the stable commutator length of elements in a surgery family is a ratio …

Study characterizes hulls and capacities on Riemannian manifolds, proving isoperimetric inequalities.

The convex hull of a set K in space consists of points which are, in a certain sense, "surrounded" by K. When K is a closed curve, we define its higher hulls, consisting of points which are "multiply surrounded" by the curve. Our main theorem shows that if a curve is knotted then it has a nonempty second hull. This pro…

New proofs given for space curves with totally positive torsion.

We introduce the notion of a ``projective hull'' for subsets of complex projective varieties, parallel to the idea of the polynomial hull in affine varieties. With this concept, a generalization of J. Wermer's classical theorem on the hull of a curve in $C^n$ is established in the projective setting. The projective hul…

Researchers link vertex algebras to non-Kähler solutions of the Hull-Strominger system.

Estimates convex hulls of smooth function images with error bounds.

Study finds knots with ideal length need not have smallest volume.

Study Hull-Strominger system and Anomaly flow on specific solvmanifolds.

New solutions found for complex structures on specific manifolds.

Study convex hulls of orbits for compact groups, defining new invariants related to polynomial degrees.

For a convex curve in an even-dimensional affine space we introduce a series of convex domains (called Young hulls), describe their structure and give a formulas fo the volume of the biggest of these domains. This paper is an attempt to generalize the classical isoperimetric inequality for the volume of the convex hull…

Proposes a faster algorithm for machine learning problems.

We study a hybrid tree-finite difference method which permits to obtain efficient and accurate European and American option prices in the Heston Hull-White and Heston Hull-White2d models. Moreover, as a by-product, we provide a new simulation scheme to be used for Monte Carlo evaluations. Numerical results show the rel…

Optimal algorithm finds if point is in convex hull of distributions.

We obtain an upper bound for the volume of the convex hull of a simple closed Frenet curve with exactly four vertices, i.e., four points of vanishing torsion, and lying on the boundary of its convex hull. Moreover, we show that the upper bound is attained when the curve intersects every plane in at most four points, a …

New flow defined to solve Hull-Strominger system, with estimates and convergence results.

Optimum in Convex Hulls (OCH) generalizes clinical trial results to broader populations.

We compute the algebraic hull of the Kontsevich-Zorich cocycle over any GL^+_2(R) invariant subvariety of the Hodge bundle, and derive from this finiteness results on such subvarieties.

We obtain the following version of Lidskii theorem. Let L, M, N be p-dimensional subspaces in R^n. Let ψ_j be the angles between L and M, let φ_j be the angles between M and N, and let θ_j be the angles between L and N. Consider the orbit of the vector ψwith respect to permutations of coordinates and inversions of axis…

We show how to construct the nonstandard hull of certain infinite-dimensional Lie algebras in order to generalize a theorem of Pestov on the enlargeability of Banach-Lie algebras. In the process, we consider a nonstandard smoothness condition on functions between locally convex spaces to ensure that the induced functio…

Estimate collapsibility of causal effects in CPDAGs via strong d-convex hulls.

Automorphisms and subdivisions of Helly graphs are studied, leading to explicit models and rational translation lengths.

Constructs examples of domains divided by groups in dimensions 3 and above.

We use twistor theory to identify the harmonic hull of an arbitrary connected open subset U of R^{2m} for m at least 2. It is the natural domain of analytic continuation in C^{2m} for harmonic functions on U.

New obstruction found for Hull-Strominger system solutions.

Sketching algorithm finds closest point on convex hull efficiently.

GraphHull models networks with clear multi-scale explanations of community structure.