arXiv research

Establishes geometric properties of elements in the positive semigroup of a general real semisimple Lie group.

Establishes a concavity property for positive Hessian quotient operators.

Study on positivity properties of vector bundle Monge-Ampère equation.

A complex disproves a curvature property.

The book is devoted to constructing embedding finite-dimensional maps into trivial bundles and investigating the corresponding general position properties.

Paper shows $L^\infty$-positivity and stochastic completeness are equivalent.

The study examines Eschenburg orbifolds with positive sectional curvature and their geometric/topological properties.

We prove that positive knots and knots with braid index three in the 3-sphere satisfy the Property P conjecture.

Collar lemma proven for certain surface group representations.

Study of new link types and their invariants, extending previous results.

Positive Thompson links are proven for oriented subgroup elements.

We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note …

In this survey article, we present some panorama of groups acting on metric spaces of non-positive curvature. We introduce the main examples and their rigidity properties , we show the links between algebraic or analytic properties of the group and geometric properties of the space. Finally, we conclude with a few conj…

The paper bounds bandwidth and focal radius for manifolds with positive isotropic curvature.

This paper describes metrics with varying curvature properties in a specific manifold.

We perform an analysis of fractal properties of the positive and the negative changes of the German DAX30 index separately using Multifractal Detrended Fluctuation Analysis (MFDFA). By calculating the singularity spectra $f(α)$ we show that returns of both signs reveal multiscaling. Curiously, these spectra display a s…

Paper proves Gromov's conjecture on manifolds with certain group properties.

The paper studies modified Einstein tensors and their positivity properties on compact manifolds.

Study finds criteria for surfaces with specific curvature properties.

Extends positive and almost positive links to successively almost positive ones.

In this paper, we study the existence and non-existence result of positive solutions to a singular elliptic equation with negative power on the bounded smooth domain or in the whole Euclidean space. Our model arises in the study of the steady states of thin films and other applied physics. We can get some useful local …

Groups with specific curvature have a regular language of geodesics.

Introduces $Θ$-positivity in Lie groups, generalizing Lusztig's positivity.

It is well known that positivity properties of the curvature of a vector bundle have implications on the algebro-geometric properties of the bundle, such as numerical positivity, vanishing of higher cohomology leading to existence of global sections etc. It is also well known that bundles arising in Hodge theory tend t…

The paper extends structure theorem to projective klt varieties with specific tangent sheaf properties.

The study explores knots and manifolds, proving properties and non-left-orderable groups.

We constructively prove the existence of time-discrete consumption processes for stochastic money accounts that fulfill a pre-specified positively homogeneous projection property (PHPP) and let the account always be positive and exactly zero at the end. One possible example is consumption rates forming a martingale und…

In this paper two metric properties on geodesic length spaces are introduced by means of the metric projection, studying their validity on Alexandrov and Busemann NPC spaces. In particular, we prove that both properties characterize the non-positivity of the sectional curvature on Riemannian manifolds. Further results …

In this paper we study numerical properties of quotients of holomorphic log-tensors.

We study a second order ordinary differential equation corresponding to rotationally symmetric $p$-harmonic maps. We show unique continuation and Liouville's type theorems for positive solutions. We discuss the existence of bounded positive entire solutions. Asymptotic properties of the positive solutions are investiga…

Paper shows regularizing flow for conical Kähler-Ricci equations.

A large class of positive finite presentations of the braid groups is found and studied. It is shown that no presentations but known exceptions in this class have the property that equivalent braid words are also equivalent under positive relations.

The article shows how to create metrics with positive Ricci curvature on twisted suspensions.

We examine geometric properties of a knot J that are unchanged by taking a (p,q)-cable K of J. Specifically, we relate w(K) to w(J), where w(K) is the width of K in the sense of Gabai. We use this information to demonstrate that thin position is a minimal bridge position of J if and only if the same is true for K, and …

The paper examines positivity properties of singular Hermitian metrics.

Study on weakly G-slim complexes and non-positive immersions for group presentations.

The paper examines functional properties on manifolds with very negative curvature.

Manifolds admitting positive sectional curvature are conjectured to have rigid homotopical structure and, in particular, comparatively small Euler charateristics. In this article, we obtain upper bounds for the Euler characteristic of a positively curved Riemannian manifold that admits a large isometric torus action. W…

For non-reversible Finsler metrics of positive flag curvature on spheres and projective spaces we present results about the number and the length of closed geodesics and about their stability properties.

Positive braids minimize knot untangling steps.

We develop the structure theory of full isometry groups of locally compact non-positively curved metric spaces. Amongst the discussed themes are de Rham decompositions, normal subgroup structure and characterising properties of symmetric spaces and Bruhat--Tits buildings. Applications to discrete groups and further dev…

We study homogenous Weyl connections with non-positive sectional curvatures. The Cartesian product $\mathbb S^1 \times M$ carries canonical families of Weyl connections with such a property, for any Riemmanian manifold $M$. We prove that if a homogenous Weyl connection on a manifold, modeled on a unimodular Lie group, …

Study on quantum $\mathfrak{sl}_3$ invariant for positive links.

The paper defines new types of positivity and proves properties of Schur forms for vector bundles.

We show that the difference between the Seifert genus and the topological 4-genus of a prime positive braid knot is bounded from below by an affine function of the minimal number of strands among positive braid representatives of the knot. We deduce that among prime positive braid knots, the property of having such a g…

Satellite links of fully positive braids are characterized.

The paper defines and studies the geometric mean for tensors and its associated Riemannian geometry.

Algebraic homology and cohomology theories for quandles have been studied extensively in recent years. With a given quandle 2(3)-cocycle one can define a state-sum invariant for knotted curves(surfaces). In this paper we introduce another version of quandle (co)homology theory, say positive quandle (co)homology. Some p…