arXiv research

Groups can embed uniformly but not act properly on contractible manifolds.

The paper proves scalar curvature decay for uniformly contractible manifolds with finite asymptotic dimension.

We show that a space with a finite asymptotic dimension is embeddable in a non-positively curved manifold. Then we prove that if a uniformly contractible manifold X is uniformly embeddable in $\R^n$ or non-positively curved n-dimensional simply connected manifold then $X\times\R^n$ is integrally hyperspherical. If a un…

We consider compact convex hypersurfaces contracting by functions of their curvature. Under the mean curvature flow, uniformly convex smooth initial hypersurfaces evolve to remain smooth and uniformly convex, and contract to points after finite time. The same holds if the initial data is only weakly convex or non-smoot…

Uniformly extend maps on Hadamard manifolds with curvature constraints.

This paper examines limits of Riemannian 2-manifolds with bounded curvature.

Optimizes long-term portfolios considering non-uniformly ergodic economic factors.

The paper shows how convex hypersurfaces contract under a specific curvature flow.

The simplicial volume of non-R^3 contractible 3-manifolds is infinite.

No 5D aspherical manifolds can have uniformly positive scalar curvature.

Curvature conditions distinguish Euclidean space and disks in contractible manifolds.

Sharp growth tightness proven for group quotients.

IFS with average shadowing property ensure chain recurrence and have specific examples.

Study finds topological restrictions on 4-manifolds with uniformly positive scalar curvature.

The paper analyzes game theory in convertible contracts during liquidity events.

Nonspin manifolds can't have uniformly positive scalar curvature.

New algorithm uniformly samples high-dimensional convex bodies efficiently.

We construct a compact metric space that has any other compact metric space as a tangent, with respect to the Gromov-Hausdorff distance, at all points. Furthermore, we give examples of compact sets in the Euclidean unit cube, that have almost any other compact set of the cube as a tangent at all points or just in a den…

New group $Q$ has unusual properties like no uniform non-amenability.

The paper proves the Generalized Smale Conjecture and contractibility of moduli spaces.

The paper studies circle packings using renormalization and subdivision rules.

Proposes a new generalization bound for Bayesian deep nets without strict assumptions.

Theory of relatively Anosov representations using flow methods.

Transformer pretraining yields strong EB performance without explicit adaptation.

We prove that the restricted holonomy group of a complete smooth solution to the Ricci flow of uniformly bounded curvature cannot spontaneously contract in finite time; it follows, then, from an earlier result of Hamilton that the holonomy group is exactly preserved by the equation. In particular, a solution to the Ric…

This paper proves properties of uniformly hyperbolic sets and constructs Markov partitions.

We develop some basic Lipschitz homotopy technique and apply it to manifolds with finite asymptotic dimension. In particular we show that the Higson compactification of a uniformly contractible manifold is mod $p$ acyclic in the finite dimensional case. Then we give an alternative proof of the Higher Signature Novikov …

Three themes of general topology: quotient spaces; absolute retracts; and inverse limits - are reapproached here in the setting of metrizable uniform spaces, with an eye to applications in geometric and algebraic topology. The results include: 1) If f: A -> Y is a uniformly continuous map, where X and Y are metric spac…

Making use of the Kerr theorem for shear-free null congruences and of Newman's representation for a virtual charge ``moving'' in complex space-time, we obtain an axisymmetric time-dependent generalization of the Kerr congruence, with a singular ring uniformly contracting to a point and expanding then to infinity. Elect…

Kähler-Ricci flow converges to Kähler-Einstein orbifold on complex surfaces.

Study on singularities of solutions to Hamilton-Jacobi equations on manifolds.

Study of Brown--York mass for four-dimensional asymptotically flat manifolds.

Geodesics found in spacetime satisfy curvature conditions.

Improved stochastic Halpern iteration for fixed-point approximation in normed spaces.

Quasi-isometries in horospherical products are close to product maps.

GCAO improves clustering of high-dimensional data by grouping low-density boundary points.

In this article, we introduce the notion of a functor on coarse spaces being coarsely excisive- a coarse analogue of the notion of a functor on topological spaces being excisive. Further, taking cones, a coarsely excisive functor yields a topologically excisive functor, and for coarse topological spaces there is an ass…

Hypothesis testing in singular models is fundamentally about identifiable vs. non-identifiable parameters.

The paper proves convergence of certain curvature flows to the origin.

Paper studies long-run risk optimization with dyadic impulses for unbounded processes.

The paper explores coalescent contractions in contractible spaces, providing criteria and examples.

New bound relaxes uniform gradient norm assumptions for PAC-Bayesian bounds.

Computable contracts simplify financial transactions and reduce legal costs.

New set type with no uniformly perfect subsets.

We prove optimal mechanisms for general contract spaces.

In an online contract selection problem there is a seller which offers a set of contracts to sequentially arriving buyers whose types are drawn from an unknown distribution. If there exists a profitable contract for the buyer in the offered set, i.e., a contract with payoff higher than the payoff of not accepting any c…

Optimal execution strategy for merger & acquisition contracts with price impact.

Study on measurable pseudo-Anosov maps on surfaces.