arXiv research

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…

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

Soap films collapse only if their bulk has negative pressure, forming convex shapes.

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

Study reduces human labeling in LLM-based classification systems.

We show that for any extreme curve in a 3-manifold M, there exist a canonical mean convex hull containing all least area disks spanning the curve. Similar result is true for asymptotic case in hyperbolic 3-space such that for any asymptotic curve, there is a canonical mean convex hull containing all minimal planes span…

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

Closed surfaces minimize total curvature in curved spaces.

We give upper bounds on the principal curvatures of a maximal surface of nonpositive curvature in three-dimensional Anti-de Sitter space, which only depend on the width of the convex hull of the surface. Moreover, given a quasisymmetric homeomorphism $φ$, we study the relation between the width of the convex hull of th…

We study the constant mean curvature (CMC) hypersurfaces in hyperbolic space whose asymptotic boundaries are closed codimension-1 submanifolds in sphere at infinity. We consider CMC hypersurfaces as generalizations of minimal hypersurfaces. We naturally generalize some notions of minimal hypersurfaces like being area m…

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…

New conditions ensure Dantzig-Wolfe relaxation matches rank-constrained optimization problems.

The paper characterizes sets with infinite hyperbolic convex hull volume.

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…

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 …

In this paper, we prove that every conformal minimal immersion of a compact bordered Riemann surface $M$ into a minimally convex domain $D\subset \mathbb{R}^3$ can be approximated, uniformly on compacts in $\mathring M=M\setminus bM$, by proper complete conformal minimal immersions $\mathring M\to D$. We also obtain a …

Develops harmonic metrics for Hull-Strominger system stability.

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

We study decomposition into simple arcs (i. e., arcs without self-intersections) for diagrams of knots and spatial graphs. In this paper, it is proved in particular that if no edge of a finite spatial graph $G$ is a knotted loop, then there exists a plane diagram $D$ of $G$ such that (i) each edge of $G$ is represented…

A new method solves convex optimization on curved spaces.

Paper develops compact formulations for optimization problems with rank-one convex functions and indicator variables.

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

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

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

The Ekeland variational principle implies what can be regarded as a strong version, in the $C^1$ category, of the Yau minimum principle: under the appropriate hypotheses {\it every} minimizing sequence admits a {\it good shadow}, a second minimizing sequence that has good properties and is asymptotic to the original on…

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 …

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 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…

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 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…

For an admissible class of smooth compact initial data sets with boundary, we prove a comparison theorem between the Wang/Liu-Yau quasi-local mass of the boundary and the Hawking mass of strictly minimizing hulls in the Jang graphs of the domain. Using this, we prove a quasi-local Penrose inequality that involves these…

While it is well known from examples that no interesting `halfspace theorem' holds for properly immersed complete $n$-dimensional self-translating mean curvature flow solitons in Euclidean space $\mathbb{R}^{n+1}$, we show that they must all obey a general `bi-halfspace theorem': Two transverse vertical halfspaces can …

A wide range of fundamental machine learning tasks that are addressed by the maximum a posteriori estimation can be reduced to a general minimum conical hull problem. The best-known solution to tackle general minimum conical hull problems is the divide-and-conquer anchoring learning scheme (DCA), whose runtime complexi…

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

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.