arXiv research

Study finite-type solutions of elliptic sinh-Gordon equation with Durham boundary conditions.

Study on self-similar sets on Riemannian manifolds with new separation conditions.

Submanifolds of coordinate finite-type were introduced in HV1. A submanifold of a Euclidean space is called a coordinate finite-type submanifold if its coordinate functions are eigenfunctions of Δ. In the present study we consider coordinate finite-type surfaces in E^4. We give necessary and sufficient conditions for g…

We prove that a class of asymptotically nonnegatively curved manifolds (in the sense of Abresch) satisfying some uniform Euclidean type volume growth conditions contains only finitely many homeomorphism types.

Study proves all free boundary CMC annuli are of finite type.

We propose a general framework for constructing and describing infinite type flat surfaces of finite area. Using this method, we characterize the range of dynamical behaviors possible for the vertical translation flows on such flat surfaces. We prove a sufficient condition for ergodicity of this flow and apply the cond…

The study classifies flows of finite curvature in 3D space.

Characterizes periodic elements in Artin-Tits groups via stability conditions.

Artin groups of finite type are not as well understood as braid groups. This is due to the additional geometric properties of braid groups coming from their close connection to mapping class groups. For each Artin group of finite type, we construct a space (simplicial complex) analogous to Teichmueller space that satis…

We prove a Frobenius-type theorem for singular distributions generated by a family of locally Lipschitz continuous vector fields satisfying almost everywhere a quantitative finite type condition.

We give a solution to the equivalence and the embedding problems for smooth CR-submanifolds of complex spaces (and, more generally, for abstract CR-manifolds) in terms of complete differential systems in jet bundles satisfied by all CR-equivalences or CR-embeddings respectively (local and global). For the equivalence p…

We show that a complete Riemannian manifold has finite topological type (i.e., homeomorphic to the interior of a compact manifold with boundary), provided its Bakry-Émery Ricci tensor has a positive lower bound, and either of the following conditions: (i) the Ricci curvature is bounded from above; (ii) the Ricci curvat…

We describe a pair of invariants for actions of finite groups on shifts of finite type, the left-reduced and right-reduced shifts. The left-reduced shift was first constructed by U. Fiebig, who showed that its zeta function is an invariant, and in fact equal to the zeta function of the quotient dynamical system. We als…

We identify branched coverings (continuous open surjections p:Y->X of Hausdorff spaces with uniformly bounded number of pre-images) with Hilbert C*-modules C(Y) over C(X) and with faithful unital positive conditional expectations E:C(Y)->C(X) topologically of index-finite type. The case of non-branched coverings corres…

Revisits conformal metrics with finite Q-curvature, providing necessary and sufficient conditions.

Conditions of Stability for explicit finite difference scheme and some results of numerical analysis for a unified 2 factor model of structural and reduced form types for corporate bonds with fixed discrete coupon are provided. It seems to be difficult to get solution formula for PDE model which generalizes Agliardi's …

In this paper we prove necessary and sufficient conditions for the Kobayashi metric on a convex domain to be Gromov hyperbolic. In particular we show that for convex domains with $C^\infty$ boundary being of finite type in the sense of D'Angelo is equivalent to the Gromov hyperbolicity of the Kobayashi metric. We also …

Given a connected, compact, totally geodesic submanifold Y^m of noncompact type inside a compact locally symmetric space of noncompact type X^n, we provide a sufficient condition that ensures that [Y^m] is nonzero in H_m(X^n; R); in low dimensions, our condition is also necessary. We provide conditions under which ther…

On contact manifolds we describe a notion of (contact) finite-type for linear partial differential operators satisfying a natural condition on their leading terms. A large class of linear differential operators are of finite-type in this sense, and for any such operator we construct a partial connection on a (finite ra…

In this paper, we give a finiteness result on the diffeomorphism types of curvature-adapted equifocal hypersurfaces in a simply connected compact symmetric space. Furthermore, the condition curvature-adapted can be dropped if the symmetric space is of rank one.

This paper investigates circle patterns with obtuse exterior intersection angles on surfaces of finite topological type. We characterise the images of the curvature maps and establish several equivalent conditions regarding long time behaviors of Chow-Luo's combinatorial Ricci flows for these patterns. As consequences,…

This is a survey on two closely related subjects. First, we review the study of topological structure of `finite type' components of spaces of Bridgeland's stability conditions on triangulated categories. The key is to understand Happel-Reiten-Smalo tilting as tiling of cells. Second, we review topological realizations…

Fixed points found in cluster modular groups under specific conditions.

The paper explores conditions for compactness and finiteness in stratified homotopy theory.

If a finite group $G$ is isomorphic to a subgroup of $SO(3)$, then $G$ has the D2-property. Let $X$ be a finite complex satisfying Wall's D2-conditions. If $π_1(X)=G$ is finite, and $χ(X) \geq 1-Def(G)$, then $X \vee S^2$ is simple homotopy equivalent to a finite $2$-complex, whose simple homotopy type depends only on …

In this note we introduce the concept of a quasi-finite complex. Next, we show that for a given countable and locally finite CW complex L the following conditions are equivalent: (i) L is quasi-finite. (ii) There exists a [L]-invertible mapping of a metrizable compactum X with e-dim X = [L] onto the Hilbert cube. Final…

In this paper, we develop a loop group description of harmonic maps $\mathcal{F}: M \rightarrow G/K$ ``of finite uniton type", from a Riemann surface $M$ into inner symmetric spaces of compact or non-compact type. This develops work of Uhlenbeck, Segal, and Burstall-Guest to non-compact inner symmetric spaces. To be mo…

New test for conditional independence using kernel embeddings.

We shall show that for a given homeomorphism type and a set of end invariants (including the parabolic locus) with necessary topological conditions which a topologically tame Kleinian group with that homeomorphism type must satisfy, there is an algebraic limit of minimally parabolic, geometrically finite Kleinian group…

We give sufficient conditions for a noncompact Riemannian manifold, which has quadratic curvature decay, to have finite topological type with ends that are cones over spherical space forms.

Lagrangian cobordisms are three-dimensional compact oriented cobordisms between once-punctured surfaces, subject to some homological conditions. We extend the Le-Murakami-Ohtsuki invariant of homology three-spheres to a functor from the category of Lagrangian cobordisms to a certain category of Jacobi diagrams. We prov…

We provide a Reifenberg type characterization for $m$-dimensional $C^1$-submanifolds of $\mathbb R^n$. This characterization is also equivalent to Reifenberg-flatness with vanishing constant combined with suitably converging approximating $m$-planes. Moreover, a sufficient condition can be given by the finiteness of th…

Study Dirac operators on finite warped cylinders with gauge fields.

The paper analyzes finite-time singularities in Spin(7)-structure flows using Shi-type estimates.

We start by showing that the finite-time absolute ruin probability in the classical risk model with constant interest force can be expressed in terms of the transition probability of a positive Ornstein-Uhlenbeck type process, say X. Our methodology applies to the case when the dynamics of the aggregate claims process …

We study spectral behavior of the complex Laplacian on forms with values in the $k^{\text{th}}$ tensor power of a holomorphic line bundle over a smoothly bounded domain with degenerated boundary in a complex manifold. In particular, we prove that in the two dimensional case, a pseudoconvex domain is of finite type if a…

Study homotopy types of 4-manifolds, finding decompositions and conditions for desuspension.

New coefficient detects irrational rotation behavior on infinite-type surfaces.

We show that tree almost automorphism groups, including Neretin groups, satisfy the analogue of the $F_\infty$-finiteness condition in the world of totally disconnected groups: They possess a cellular action on a contractible cellular complex such that the stabilizers are open and compact and the restriction of the act…

Let G be a Chevalley group scheme and B<=G a Borel subgroup scheme, both defined over Z. Let K be a global function field, S be a finite non-empty set of places over K, and O_S be the corresponding S-arithmetic ring. Then, the S-arithmetic group B(O_S) is of type F_{|S|-1} but not of type FP_{|S|}. Moreover one can der…

A Garside group is a group admitting a finite lattice generating set D. Using techniques developed by Bestvina for Artin groups of finite type, we construct K(π,1)s for Garside groups. This construction shows that the (co)homology of any Garside group G is easily computed given the lattice D, and there is a simple suff…

Generalizes $π_2$-diffeomorphism finiteness to non-zero first homotopy groups.

Finite-dimensional spaces of biharmonic functions on manifolds are explored.

The paper develops finite knot theory using ropelength-filtered Reidemeister graphs.

Study tests whether trade-off functions are above or below benchmarks using finite samples.

The set SL(n) of n-string links has a monoid structure, given by the stacking product. When considered up to concordance, SL(n) becomes a group, which is known to be abelian only if n=1. In this paper, we consider two families of equivalence relations which endow SL(n) with a group structure, namely the C_k-equivalence…

We study some equivalent properties of the curvature-dimension conditions $CD(n,K)$ inequality on infinite, but locally finite graph. These equivalences are gradient estimate, Poincaré type inequalities and reverse Poincaré inequalities. And we also obtain one equivalent property of gradient estimate for a new notion o…

Conditions for simple closed curves in surface covers.