arXiv research

Criterion for stopping conjugacy class enumeration in triangle groups.

New invariant for hyperbolic surfaces, geometric criterion for domains.

Clarifies boundary criterion for non-one-ended subgroups in cubulation theory.

Let X be a complex projective variety and D a reduced divisor on X. Under a natural minimal condition on the singularities of the pair (X, D), which includes the case of smooth X with simple normal crossing D, we ask for geometric criteria guaranteeing various positivity conditions for the log-canonical divisor K_X+D. …

Existence of a conjugate point in the incompressible Euler flow on a sphere and an ellipsoid is considered. Misiolek (1996) formulated a differential-geometric criterion (we call M-criterion) for the existence of a conjugate point in a fluid flow. In this paper, it is shown that no zonal flow (stationary Euler flow) sa…

New criterion for Weyl law on Riemannian manifolds without standard assumptions.

We inspect Vietoris-Rips complexes $VR_t(X)$ of certain metric spaces $X$ using a new generalization of Bestvina-Brady discrete Morse theory. Our main result is a pair of metric criteria on $X$, called the Morse Criterion and Link Criterion, that allow us to deduce information about the homotopy types of certain $VR_t(…

The paper analyzes and proposes a new stopping criterion for recursive Bayesian classification.

Criterion for surfaces in Heisenberg group to be graphs using flat cones.

Proposes a new criterion for selecting Nash equilibria considering both utility and inequality.

Study on stable minimal hypersurfaces under Ricci curvature constraints.

The study provides a criterion for diffeomorphism via long-time Ricci flow.

This note will prove a discreteness criterion for groups of orientation-preserving isometries of the hyperbolic space which contain a parabolic element. It can be viewed as a generalization of the well-known results of Shimizu-Leutbecher and Jorgensen in dimensions 2 and 3, and is closely related to Waterman's inequali…

In the first part of this paper, we consider smooth maps from a compact orientable 3-manifold without boundary to the 2-sphere. We give a geometric criterion to decide whether two given maps are homotopic, based on the sets of points where the maps are equal or antipodal. We extend this criterion to non-singular vector…

Subdivision rules create sequences of nested cell structures on CW-complexes, and they frequently arise from groups. In this paper, we develop several tools for classifying subdivision rules. We give a criterion for a subdivision rule to represent a Gromov hyperbolic space, and show that a subdivision rule for a hyperb…

We propose an algebraic geometric stability criterion for a polarised variety to admit an extremal Kaehler metric. This generalises conjectures by Yau, Tian and Donaldson which relate to the case of Kaehler-Einstein and constant scalar curvature metrics. We give a result in geometric invariant theory that motivates thi…

We give a geometric criterion which shows p-parabolicity of a class of submanifolds in a Riemannian manifold, with controlled second fundamental form, for p bigger or equal than 2.

We establish a criterion for certain mapping classes of a surface homeomorphisms to be pseudo-Anosov in terms of the geometry of hyperbolic 3-manifolds and Gromov-hyperbolic surface group extensions. Specifically, any element of the fundamental group of a surface S gives rise to a mapping class on the punctured surface…

We construct an example of a uniquely ergodic measured foliation on a surface such that the associated translation flow on the orientation double cover is minimal but not uniquely ergodic. We then prove a geometric criterion for the horizontal foliation of a quadratic differential to be uniquely ergodic. The second the…

Support Vector Data Description (SVDD) is a machine-learning technique used for single class classification and outlier detection. SVDD formulation with kernel function provides a flexible boundary around data. The value of kernel function parameters affects the nature of the data boundary. For example, it is observed …

The paper establishes pressure gaps for manifolds with flat subtori singularities.

We shall develop a new deformation theory of geometric structures in terms of closed differential forms. This theory is a generalization of Kodaira -Spencer theory and further we obtain a criterion of unobstructed deformations. We apply this theory to certain geometric structures: Calabi-Yau, HyperKähler, $\G$ and $\Sp…

A new criterion selects models in overparameterized settings.

The paper studies the modified J-equation on Kähler manifolds.

New stability criterion for Fano manifolds using anticanonically balanced metrics.

Paper bounds surface diameter and solves Plateau-Douglas problem.

Profinite rigidity proven for many hyperbolic manifolds.

GCNNs on homogeneous spaces use vector bundles and Hilbert spaces.

In this paper, we give a complete criterion for a discrete faithful representation $ρ:F_n \ra \pslc$ to be primitive stable. This will answer Minsky's conjectures about geometric conditions on $\H^3/ρ(F_n)$ regarding the primitive stability of $ρ$.

SIC detects elbows in error curves automatically.

We introduce an operation that measures the self intersections of paths on a surface. As applications, we give a criterion of the realizability of a generalized Dehn twist, and derive a geometric constraint on the image of the Johnson homomorphism.

The recently introduced dropout training criterion for neural networks has been the subject of much attention due to its simplicity and remarkable effectiveness as a regularizer, as well as its interpretation as a training procedure for an exponentially large ensemble of networks that share parameters. In this work we …

The study extends Dehn filling to Lie groups, ensuring geometric properties.

Alternative solvability criterion for minimal surface equations and mean curvature flow.

The Cannon Conjecture from the geometric group theory asserts that a word hyperbolic group that acts effectively on its boundary, and whose boundary is homeomorphic to the 2-sphere, is isomorphic to a Kleinian group. We prove the following Criterion for Cannon's Conjecture: A hyperbolic group $G$ (that acts effectively…

Criteria for sharksfin and deltoid singularities from plane to plane, with applications.

In this study, a pairwise comparison matrix is generalized to the case when coefficients create Lie group $G$, non necessarily abelian. A necessary and sufficient criterion for pairwise comparisons matrices to be consistent is provided. Basic criteria for finding a nearest consistent pairwise comparisons matrix (extend…

We make a systematic study of the Hilbert-Mumford criterion for different notions of stability for polarised algebraic varieties $(X,L)$; in particular for K- and Chow stability. For each type of stability this leads to a concept of slope $μ$ for varieties and their subschemes; if $(X,L)$ is semistable then $μ(Z)\leμ(X…

This is a survey of our research on geometric structures of projective embeddings and includes some topics of our talks in several symposia during 1990-99. We clarify our main problem, which is to construct a kind of geometric composition series of projective embeddings. The concept of "geometric composition series" is…

This paper continues our study, initiated in [arXiv:1108.3370], of essential state surfaces in link complements that satisfy a mild diagrammatic hypothesis (homogeneously adequate). For hyperbolic links, we show that the geometric type of these surfaces in the Thurston trichotomy is completely determined by a simple gr…

Optimized Franz-Parisi criterion matches SQ lower bounds for various statistical models.

We give a simple analytic criterion which characterizes linearizable 1-codimensional webs. Then we give an invariant geometrical interpretation of it, in term of projective connection. We explain then how our approach allows to study linearization of more general objects than 1-codimensional webs. By way of illustratio…

We identify the difference between the CM polarisation and the Chow polarisation on the ``Hilbert scheme''. As a consequence, we give a numerical criterion for the CM stability as in Mumfords' G.I.T.. Also, we write down an explicit formula for the generalised futaki invariant interms of weights and multiplicities of t…

Analytic completeness criterion applied to constant mean curvature surfaces.

We propose two related unsupervised clustering algorithms which, for input, take data assumed to be sampled from a uniform distribution supported on a metric space $X$, and output a clustering of the data based on the selection of a topological model for the connected components of $X$. Both algorithms work by selectin…

We develop a general framework for applying the Kelly criterion to stock markets. By supplying an arbitrary probability distribution modeling the future price movement of a set of stocks, the Kelly fraction for investing each stock can be calculated by inverting a matrix involving only first and second moments. The fra…

Support Vector Data Description (SVDD) provides a useful approach to construct a description of multivariate data for single-class classification and outlier detection with various practical applications. Gaussian kernel used in SVDD formulation allows flexible data description defined by observations designated as sup…

Unified geometric scattering model for measure spaces.