arXiv research

Study linear perturbations of Spin(7) metrics, finding only rank one nilpotent matrices.

Study metric perturbations to make degenerate harmonic forms non-degenerate.

The paper constructs new bimetric conformal invariants using metric perturbations.

The paper shows how to stabilize perturbed Kähler-Ricci solitons.

Stability of submanifold cut loci under metric perturbations proved.

The paper proves conditions for Kähler-Einstein metrics to remain Kähler-Einstein under cscK perturbations.

Ricci flow simulations show unstable Fubini-Study metrics develop singularities.

New metrics improve scRNA-seq perturbation modeling by reducing mode collapse.

We developed a perturbation model for affine gravity theories.

Estimates mass of static vacuum metrics with small Bartnik data.

Stability of cut locus under metric perturbations in compact Riemannian manifolds.

In this short note, we prove that conformal classes which are small perturbations of a product conformal class on a product with a standard sphere admit a metric extremal for some Laplace eigenvalue. As part of the arguments we obtain perturbed harmonic maps with constant density.

Prove that collapsing CSC metrics can be perturbed to invariant collapsing CSC metrics.

Study magnetic perturbations in Riemannian and Lorentzian Calderón problems.

This paper introduces metrics to evaluate robustness of neural networks to natural adversarial examples.

We prove a theorem which asserts that the Lie algebra of all holomorphic vector fields on a compact Kähler manifold with a perturbed extremal metric has the structure similar to the case of an unperturbed extremal Kähler metric proved by Calabi.

Estimates for harmonic forms on a 3-Torus, proving their existence.

Complete Calabi-Yau metrics made on special 3D spaces.

Study reveals class-dependent effects in perturbation-based feature attribution metrics for time series classification.

We construct continuous families of scattering manifolds with the same scattering phase. The manifolds are compactly supported metric perturbations of Euclidean $\mathbf{R}^{n}$ for $n\geq8$. The metric perturbation may have arbitrarily small support.

We show that a small perturbation of the boundary distance function of a simple Finsler metric on the $n$-disc is also the boundary distance function of some Finsler metric. (Simple metric form an open class containing all flat metrics.) The lens map is map that sends the exit vector to the entry vector as a geodesic c…

We prove that in many cases the existence of an extremal metric for some Laplace eigenvalue in a conformal class allows to find extremal metrics in conformal classes close by. As a consequence and as part of the arguments we obtain perturbed harmonic maps with constant density.

3D spherical caps are rigid under certain perturbations.

The celebrated KAM Theory says that if one makes a small perturbation of a non-degenerate completely integrable system, we still see a huge measure of invariant tori with quasi-periodic dynamics in the perturbed system. These invariant tori are known as KAM tori. What happens outside KAM tori draws a lot of attention. …

We study the (massless) Dirac operator on a 3-sphere equipped with Riemannian metric. For the standard metric the spectrum is known. In particular, the eigenvalues closest to zero are the two double eigenvalues +3/2 and -3/2. Our aim is to analyse the behaviour of eigenvalues when the metric is perturbed in an arbitrar…

Tseytlin has recently proposed that an action functional exists whose gradient generates to all orders in perturbation theory the Renormalization Group (RG) flow of the target space metric in the worldsheet sigma model. The gradient is defined with respect to a metric on the space of coupling constants which is explici…

Paper shows perturbed Taub-Bolt metric becomes singularity under Ricci flow.

We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.

Paper proposes a robust metric learning algorithm.

Eigenvalues of Steklov eigenproblems change predictably with boundary tweaks.

Study shows current metrics for audio adversarial examples are unreliable for human perception.

We prove the equivalences of several classical complete metrics on the Teichmüller and the moduli spaces of Riemann surfaces. We use as bridge two new Kähler metrics, the Ricci metric and the perturbed Ricci metric and prove that the perturbed Ricci metric is a complete Kähler metric with bounded negative holomorphic s…

Proposes a text perturbation method using a Mahalanobis metric to balance privacy and utility.

Einstein manifolds are rigid under certain metric deformations.

Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigen…

We study the perturbations of two classes of static black ellipsoid solutions of four dimensional vacuum Einstein equations. Such solutions are described by generic off--diagonal metrics which are generated by anholonomic transforms of diagonal metrics. The analysis is performed in the approximation of small eccentrici…

Among all conformal classes of Riemannian metrics on ${\Bbb CP}_2$, that of the Fubini-Study metric is shown to have the largest Yamabe constant. The proof, which involves perturbations of the Seiberg-Witten equations, also yields new results on the total scalar curvature of almost-Kähler 4-manifolds.

In this paper we prove the Penrose inequality for metrics that are small perturbations of the Schwarzschild anti-de Sitter metrics of positive mass. We use the existence of a global foliation by weakly stable constant mean curvature spheres and the monotonicity of the Hawking mass.

Counts minimal tori in Riemannian manifolds with 6 or more dimensions.

Let $M$ a compact connected orientable 4-manifold. We study the space $Ξ$ of $Spin^c$-structures of fixed fundamental class, as an infinite dimensional principal bundle on the manifold of riemannian metrics on $M$. In order to study perturbations of the metric in Seiberg-Witten equations, we study the transversality of…

This paper studies the normalized Ricci flow from a slight perturbation of the hyperbolic metric on $\mathbb H^n$. It's proved that if the perturbation is small and decays sufficiently fast at the infinity, then the flow will converge exponentially fast to the hyperbolic metric when the dimension $n>5$.

We compute the Ricci curvature of a curved noncommutative three torus. The computation is done both for conformal and non-conformal perturbations of the flat metric. To perturb the flat metric, the standard volume form on the noncommutative three torus is perturbed and the corresponding perturbed Laplacian is analyzed.…

Paper introduces metrics for evaluating multi-agent policies using best response dynamics.

Paper examines stability of Bayesian posterior measures using integral probability metrics.

New metrics produce discrete zero sets for nondegenerate harmonic forms.

The paper defines and analyzes Kähler metrics near a compact manifold, showing their deviation from Poincaré-type metrics.

PerturBench benchmarks ML models for cellular perturbation analysis.

We construct new examples of Einstein metrics by perturbing the conformal infinity of geometrically finite hyperbolic metrics and by applying the inverse function theorem in suitable weighted Hölder spaces.