arXiv research

The paper defines a new equivalence relation for knot projections and finds an infinite number of distinct classes.

Every weak Perron number is realized as a stretch factor of a homeomorphism on a surface.

Classifies compact spaces by shape, finite spaces by weak homotopy.

Survey of recent results in weak almost contact structures.

Study on a new type of manifolds that generalize almost C-manifolds.

We describe various equivalent ways of associating to an orbifold, or more generally a higher étale differentiable stack, a weak homotopy type. Some of these ways extend to arbitrary higher stacks on the site of smooth manifolds, and we show that for a differentiable stack X arising from a Lie groupoid G, the weak homo…

Survey of weak metric f-manifolds, generalizing K. Yano's structures.

The paper studies a new structure on contact manifolds and its foliation properties.

Motivated by the usefulness of boundaries in the study of hyperbolic and CAT(0) groups, Bestvina introduced a general approach to group boundaries via the notion of a Z-structure on a group G. Several variations on Z-structures have been studied and existence results have been obtained for some very specific classes of…

This paper proves that one-relator groups have a weak Z-structure.

Study weak $f$-K-contact manifolds, finding Einstein-type metrics and solitons.

We probe the character of knotting in open, confined polymers, assigning knot types to open curves by identifying their projections as virtual knots. In this sense, virtual knots are transitional, lying in between classical knot types, which are useful to classify the ambiguous nature of knotting in open curves. Modell…

The study examines conditions for weak nearly cosymplectic manifolds to split into products.

Study validates Michor-Mumford conjecture in infinite dimensional Hilbertian H-type groups.

Researchers extend period maps for Calabi-Yau types using modified Kato-Nakayama-Usui construction.

Study proves existence of weak mean curvature flow with contact angle.

Proves PL cobordism category's homotopy type, analogous to smooth case.

Study approximates weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.

The paper characterizes Sasakian manifolds using weak nearly Sasakian structures.

Develops Poisson structures on weak Sobolev loop spaces for integrable systems.

Using the weak solution of Inverse mean curvature flow, we prove the sharp Minkowski-type inequality for outward minimizing hypersurfaces in Schwarzschild space.

New homotopy types and invariants defined for knots.

Paper introduces methods for more reliable probabilistic predictions with confidence intervals.

We detail the construction of a weak Poisson bracket over a submanifold of a smooth manifold M with respect to a local foliation of this submanifold. Such a bracket satisfies a weak type Jacobi identity but may be viewed as a usual Poisson bracket on the space of leaves of the foliation. We then lift this weak Poisson …

In this paper we introduce a general notion of weak extension property for embeddings induced by a group actions. As an example, for the group H(M, m) of measure-preserving homeomorphisms of a noncompact manifold M, we deduce weak type extension theorems, and as an application we exhibit the local contractibility of th…

The paper finds the Finsler structure of Apollonian weak metric on unit disc.

Transcendental holomorphic Morse inequalities aim at characterizing the positivity of transcendental cohomology classes of type $(1,1)$. In this paper, we prove a weak version of Demailly's conjecture on transcendental Morse inequalities on compact Kähler manifolds. And as a consequence, we partially improve a result o…

We define and study metrics and weak metrics on the Teichmueller space of a surface of topologically finite type with boundary. These metrics and weak metrics are associated to the hyperbolic length spectrum of simple closed curves and of properly embedded arcs in the surface. We give a comparison between the defined m…

The study examines different types of equilibria for stopping problems in one-dimensional diffusion processes.

Bayesian priors improve neural network performance on weak signals.

We define virtual braid groups of type B and construct a morphism from such a group to the group of isomorphism classes of some invertible complexes of bimodules up to homotopy.

Atiyah classes of DG manifolds of positive amplitude are invariant under weak equivalences.

Study the spaces of flat connections for classical Lie groups using Chern-Weil theory.

Regression problems assume every instance is annotated (labeled) with a real value, a form of annotation we call \emph{strong guidance}. In order for these annotations to be accurate, they must be the result of a precise experiment or measurement. However, in some cases additional \emph{weak guidance} might be given by…

We show a very general existence theorem to the complex Monge-Ampère type equation on hyperconvex domains.

In this paper, we study general $(α,β)$-metrics which $α$ is a Riemannian metric and $β$ is an one-form. We have proven that every weak Landsberg general $(α,β)$-metric is a Berwald metric, where $β$ is a closed and conformal one-form. This show that there exist no generalized unicorn metric in this class of general $(…

This article analyzes the weak error of SGD optimization schemes.

We show a general existence theorem to the complex Monge-Ampère type equation on compact Kähler manifolds.

The paper defines new homotopy relations on knot projections and classifies certain knot types.

The paper gives the complete characterization of all graded nilpotent Lie algebras with infinite-dimensional Tanaka prolongation as extensions of graded nilpotent Lie algebras of lower dimension by means of a commutative ideal. We introduce a notion of weak characteristics of a vector distribution and prove that if a b…

We consider remodeling the planar search patterns, in the presence of the river-type perturbation represented by the weak vector field, basing on the time-optimal paths as Finslerian solutions to the Zermelo navigation problem via Randers metric.

W2S FT often outperforms weak teachers due to low intrinsic dimensionality.

We determine an explicit presentation by generators and relations of the cohomology algebra $H^*(\mathbb P^2\setminus C,\mathbb C)$ of the complement to an algebraic curve $C$ in the complex projective plane $\mathbb P^2$, via the study of log-resolution logarithmic forms on $\mathbb P^2$. As a first consequence, we de…

The problem of prescribing conformally the scalar curvature of a closed Riemannian manifold as a given Morse function reduces to solving an elliptic partial differential equation with critical Sobolev exponent. Two ways of attacking this problem consist in subcritical approximations or negative pseudo gradient flows. W…

A new definition of continuous-time equilibrium controls is introduced. As opposed to the standard definition, which involves a derivative-type operation, the new definition parallels how a discrete-time equilibrium is defined, and allows for unambiguous economic interpretation. The terms "strong equilibria" and "weak …

Long time existence and convergence to a circle is proved for radial graph solutions to a mean curvature type curve flow in warped product surfaces (under a weak assumption on the warp potential of the surface). This curvature flow preserves the area enclosed by the evolving curve, and this fact is used to prove a gene…

In the category of metrics with conical singularities along a smooth divisor with angle in $(0, 2π)$, we show that locally defined weak solutions ($C^{1,1}-$solutions) to the Kähler-Einstein equations actually possess maximum regularity, which means the metrics are actually Hölder continuous in the singular polar coord…

Proves smoothness and star-shapedness of weak IMCF solutions in hyperbolic space.