arXiv research

We generalize the bifurcation technique of Bando-Mabuchi in the context of extremal metrics.

Study expands harmonic almost contact metric structures classification.

The paper explores metrics and models for analyzing biological shapes.

We discuss the problem of prescribing the mean curvature and conformal class as boundary data for Einstein metrics on 3-manifolds, in the context of natural elliptic boundary value problems for Riemannian metrics.

New algorithm reduces regret in contextual bandits with many near-boundary contexts.

The paper connects counterfactual fairness to robust prediction and group fairness using causal context.

Spatially-aware metrics improve uncertainty evaluation in segmentation.

We show that both, the Jordan curve theorem and the Schoenflies theorem extend to non-metric manifolds (at least in the two-dimensional context), and conclude by some dynamical applications à la Poincaré-Bendixson.

New metric measure space theory for Lipschitz constants.

The paper studies projectively equivalent para-Kaehler metrics in 4D.

We study branched covering spaces in several contexts, proving that under suitable circumstances the cover satisfies the same upper curvature bounds as the base space. The first context is of a branched cover of an arbitrary metric space that satisfies Alexandrov's curvature condition CAT(k), over an arbitrary complete…

We characterize the convexity of functions and the monotonicity of vector fields on metric measure spaces with Riemannian Ricci curvature bounded from below. Our result offers a new approach to deal with some rigidity theorems such as `splitting theorem' and `volume cone implies metric cone theorem' in non-smooth conte…

Study characterizes Einstein metrics in warped product spaces.

Algorithm learns similarities to optimize bandit decisions in unknown metric space.

Survey on complex Monge-Ampère equations in Hermitian contexts.

On connected manifolds of dimension higher than three, the non-existence of $132$ Chinea and González-Dávila types of almost contact metric structures is proved. This is a consequence of some interrelations among components of the intrinsic torsion of an almost contact metric structure. Such interrelations allow to des…

Suppose $(X,ω)$ is a compact Kähler manifold. Following Mabuchi, the space of smooth Kähler potentials $\mathcal H$ can be endowed with a Riemannian structure, which induces an infinite dimensional path length metric space $(\mathcal H,d)$. We prove that the metric completion of $(\mathcal H,d)$ can be identified with …

This paper is a survey of some of the developments in coarse extrinsic geometry since its inception in the work of Gromov. Distortion, as measured by comparing the diameter of balls relative to different metrics, can be regarded as one of the simplist extrinsic notions. Results and examples concerning distorted subgrou…

We study harmonic almost contact structures in the context of contact metric manifolds, and an analysis is carried out when such a manifold fibres over an almost Hermitian manifold, as exemplified by the Boothby-Wang fibration. Two types of almost contact metric warped products are also studied, relating their harmonic…

In this note we use the Calabi ansatz, in the context of metrics with conical singularities along a divisor, to produce regular Calabi-Yau cones and Kähler-Einstein metrics of negative Ricci with a cuspidal point. As an application, we describe singularities and cuspidal ends of the completions of the complex hyperboli…

We provide an algebraic framework for quantization of Hermitian metrics that are solutions of the Hitchin equation for Higgs bundles over a projective manifold. Using Geometric Invariant Theory, we introduce a notion of balanced metrics in this context. We show that balanced metrics converge at the quantum limit toward…

Multi-task learning (MTL) improves prediction performance in different contexts by learning models jointly on multiple different, but related tasks. Network data, which are a priori data with a rich relational structure, provide an important context for applying MTL. In particular, the explicit relational structure imp…

ContextFlow++ improves generative models by conditioning on mixed-variable contexts.

We reformulate the compatibility condition between a generalized metric and a small (non-maximal rank) Dirac structure in an exact Courant algebroid found in the context of the gauging of strings and formulated by means of two connections in purely Dirac-geometric terms. The resulting notion, a transverse generalized m…

A variety of machine learning models have been proposed to assess the performance of players in professional sports. However, they have only a limited ability to model how player performance depends on the game context. This paper proposes a new approach to capturing game context: we apply Deep Reinforcement Learning (…

This paper introduces C-DSL to improve data mining outcomes by considering context.

In the algebraic context, we show that null Osserman, spacelike Osserman, and timelike Osserman are equivalent conditions for a model of signature (2,2). We also classify the null Jordan Osserman models of signature (2,2). In the geometric context, we show that a pseudo-Riemannian manifold of signature (2,2) is null Jo…

Proposes a method to select fair performance metrics through metric elicitation.

We derive the Chern-Gauss-Bonnet Theorem for manifolds with smooth non-degenerate boundary in the pseudo-Riemannian context from the corresponding result in the Riemannian setting by examining the Euler-Lagrange equations associated to the Pfaffian of a complex "metric" on the tangent space and then applying analytic c…

Proves inequality in metric measure spaces with non-branching structure.

Generalized Kahler geometry is the natural analogue of Kahler geometry, in the context of generalized complex geometry. Just as we may require a complex structure to be compatible with a Riemannian metric in a way which gives rise to a symplectic form, we may require a generalized complex structure to be compatible wit…

We prove an optimal systolic inequality for CAT(0) metrics on a genus~2 surface. We use a Voronoi cell technique, introduced by C.~Bavard in the hyperbolic context. The equality is saturated by a flat singular metric in the conformal class defined by the smooth completion of the curve y^2=x^5-x. Thus, among all CAT(0) …

The paper developes a geometrization of a Kronecker $h$-regular vertical fundamental metrical d-tensor $G^{(α)(β)}_{(i)(j)}$ on the jet fibre bundle of order one $J^1(T,M)$. This geometrization gives a mathematical model for both gravitational and electromagnetic field theory, in a general setting. In this context, the…

Study compares metrics from negative curvature and quasi-Fuchsian representations.

We study adaptive data-dependent dimensionality reduction in the context of supervised learning in general metric spaces. Our main statistical contribution is a generalization bound for Lipschitz functions in metric spaces that are doubling, or nearly doubling. On the algorithmic front, we describe an analogue of PCA f…

New metric and method for sEMG-based gesture recognition under domain shifts.

New criteria for non-isometric group actions in metric spaces.

Given a compact complex $n$-fold $X$ satisfying the $\partial\bar\partial$-lemma and supposed to have a trivial canonical bundle $K_X$ and to admit a balanced (=semi-Kähler) Hermitian metric $ω$, we introduce the concept of deformations of $X$ that are {\bf co-polarised} by the balanced class $[ω^{n-1}]\in H^{n-1,\,n-1…

We investigate the class of geodesic metric discs satisfying a uniform quadratic isoperimetric inequality and uniform bounds on the length of the boundary circle. We show that the closure of this class as a subset of Gromov-Hausdorff space is intimately related to the class of geodesic metric disc retracts satisfying c…

Study creates web interface to elicit user-preferred metrics.

The paper introduces contexture theory to characterize representation learning from contexts.

The paper studies metrics on hyperkähler manifolds using sub-twistor constraints.

We present the linearized metrizability problem in the context of parabolic geometries and subriemannian geometry, generalizing the metrizability problem in projective geometry studied by R. Liouville in 1889. We give a general method for linearizability and a classification of all cases with irreducible defining distr…

In the context of Thurstons geometrisation program we address the question which compact aspherical 3-manifolds admit Riemannian metrics of nonpositive curvature. We show that non-geometric Haken manifolds generically, but not always, admit such metrics. More precisely, we prove that a Haken manifold with, possibly emp…

Proportional centroid clustering aims to fairly group points without prior protected subsets.

The main result of this note is that, for each $n\in \{1,2,3,\ldots\}$, there exists a Hodge metric on the $n$-th Hirzebruch surface whose positive holomorphic sectional curvature is $\frac{1}{(1+2n)^2}$-pinched. The type of metric under consideration was first studied by Hitchin in this context. In order to address th…

AI benchmarks evaluate football team performance using generative models.

The paper explores how magnetic systems' spectra can identify metrics and 1-forms.