arXiv research

DPNs learn pose-invariant object representations.

Introduces Witten deformation and its applications in topology.

Study examines deformations of Kerr-(A)dS near horizon geometry.

Paper discusses star products and Kähler metrics, linking deformation quantization and constant curvature metrics.

The paper studies deformations and confluences of singularities in meromorphic connections and quadratic differentials.

In this paper, we construct spines, i.e., $\Mod_g$-equivariant deformation retracts, of the Teichmüller space $\T_g$ of compact Riemann surfaces of genus $g$. Specifically, we define a $\Mod_g$-stable subspace $S$ of positive codimension and construct an intrinsic $\Mod_g$-equivariant deformation retraction from $\T_g$…

We obtain a formal obstruction, i.e. a necessary condition for the existence of polarised complex deformations of Kähler-Ricci solitons. This obstruction is expressed in terms of the harmonic part of the variation of the complex structure.

The thesis explores integrable systems and rigidity in PDEs with symmetry.

The germ of the universal isomonodromic deformation of a logarithmic connection on a stable n-pointed genus g curve always exists in the analytic category. The first part of this paper investigates under which conditions it is the analytic germification of an algebraic isomonodromic deformation. Up to some minor techni…

Geometric interpretation of 2d-4d wall-crossing formulas.

In the first part of this article we provide a geometrically oriented approach to the theory of orbispaces which originally had been introduced by Chen. We explain the notion of a vector orbibundle and characterize the good sections of a reduced vector orbibundle as the smooth stratified sections. In the second part of…

Margulis space-times with parabolic holonomy elements are stable under sufficiently small deformations.

The thesis explores dualities and gaugings in supergravity theories.

In this article we give the realization of the Klein's Program for geometrical structures (Riemannian spaces and fiber bundles with connection) with arbitrary variable curvature within the framework of infinite deformed groups. These groups generalize gauge groups to the case of nontrivial action on the base space of b…

The paper studies deformations of Calabi-Yau manifolds using Gauduchon metrics.

Motivated by a remark and a question of Nicholas Katz, we characterize the tangent space of the space of Fuchsian equations with given generic exponents inside the corresponding moduli space of logarithmic connections: we construct a weight 1 Hodge structure on the tangent space of the moduli of logarithmic connections…

Every rack $Q$ provides a set-theoretic solution $c_Q$ of the Yang-Baxter equation. This article examines the deformation theory of $c_Q$ within the space of Yang-Baxter operators over a ring $\A$, a problem initiated by Freyd and Yetter in 1989. As our main result we classify deformations in the modular case, which ha…

Localized deformation of scalar curvature and mean curvature on manifolds.

The paper explores the correspondence between gradient flow lines of a function and its Lagrange multiplier functional.

The paper finds global Darboux coordinates for a new family of symplectic forms on the deformation space of $\mathbb{R}\mathbb{P}^2$-structures.

We prove 3-dimensional hyperbolic cone-manifolds are geometrically inflexible: a cone-deformation of a hyperbolic cone-manifold determines a bi-Lipschitz diffeomorphism between initial and terminal manifolds in the deformation in the complement of a standard tubular neighborhood of the cone-locus whose pointwise bi-Lip…

In the first part we survey some of the known results and conjectures on compact Hyperkaehler (HK) manifolds. In the second part we presents a program which aims to show that HK four-folds whose second cohomology (with 4-tuple cup-product) is isomorphic to that of the Hilbert square of a K3 enjoy many of the beautiful …

We study deformations of complex hyperbolic surfaces which furnish the simplest examples of: (i) negatively curved Kähler manifolds and (ii) negatively curved Riemannian manifolds not having {\it constant} curvature. Although such complex surfaces may share the rigidity of quaternionic/octionic hyperbolic manifolds, ou…

DeformRS certifies deep networks against various input deformations.

Special Lagrangian submanifolds are submanifolds of a Calabi-Yau manifold calibrated by the real part of the holomorphic volume form. In this paper we use elliptic theory for edge-degenerate differential operators on singular manifolds to study the moduli space of deformations of special Lagrangian submanifolds with ed…

Proved contractibility of geodesic triangulation space on hyperbolic surfaces.

Estimates deformation of elastic objects using neural networks from few observations.

Pooling is not essential for image classification stability.

The paper proves convergence of WDVV potentials and semisimplicity of Frobenius manifolds.

Study properties of holomorphic $p$-contact manifolds, including non-Kähler hyperbolicity and deformations.

The paper studies properties of a second-order tangent bundle with a deformed metric.

This paper is a continuation of the previous paper of the author[M]. We show that an affine deformation space of a hyperbolic surface of type (g,b) can be parametrized by Margulis invariants and affine twist parameters with a certain decomposition of the surface, which are associated with the Fenchel-Nielsen coordinate…

A behavior of extreme networks under deformations of their boundary sets is investigated. It is shown that analyticity of a deformation of boundary set guarantees preservation of the networks types for minimal spanning trees, minimal fillings and so-called stable shortest trees in the Euclidean space.

We examine the dependence of the deformation obtained by bending quasi-Fuchsian structures on the bending lamination. We show that when we consider bending quasi-Fuchsian structures on a closed surface, the conditions obtained by Epstein and Marden to relate weak convergence of arbitrary laminations to the convergence …

In Part I, we develop the notions of a Moebius structure and a conformal Cartan geometry, establish an equivalence between them; we use them in Part II to study submanifolds of conformal manifolds in arbitrary dimension and codimension. We obtain Gauss-Codazzi-Ricci equations and a conformal Bonnet theorem characterizi…

This paper consists of two parts. In the first one we study the behaviour of medial axes (skeletons) of closed sets in a connected complete Riemannian manifold $\mathcal{M}$ under deformations. The second one is devoted to a similar study of conflict sets. We apply a new approach to the deformation process. Instead of …

The paper provides explicit bilipschitz bounds on Dehn fillings of hyperbolic 3-manifolds.

Proposes differential and integral invariants under Mobius transformation.

In two former papers, the authors independently proved that the space of hyperbolic cone-3-manifolds with cone angles less than 2π and fixed singular locus is locally parametrized by the cone angles. In this sequel, we investigate the local shape of the deformation space when the singular locus is no longer fixed, i.e.…

Extends noncommutative deformations of holomorphic line bundles on complex tori and their mirror partners.

We construct a simply connected minimal complex surface of general type with $p_g=0$ and $K^2=2$ which has an involution such that the minimal resolution of the quotient by the involution is a simply connected minimal complex surface of general type with $p_g=0$ and $K^2=1$. In order to construct the example, we combin…

Deep learning automates LV segmentation in cardiac MRI.

This paper goes some way in explaining how to construct an integrable hierarchy of flows on the space of conformally immersed tori in n-space. These flows have first occured in mathematical physics -- the Novikov-Veselov and Davey-Stewartson hierarchies -- as kernel dimension preserving deformations of the Dirac operat…

Researchers prove spectral rigidity of Liouville tori under specific conditions.

Paper removes singularities from compact area minimizers in positive scalar curvature manifolds.

We consider the second variational derivative of a given gauge-natural invariant Lagrangian taken with respect to (prolongations of) vertical parts of gauge-natural lifts of infinitesimal principal automorphisms. By requiring such a second variational derivative to vanish, {\em via} the Second Noether Theorem we find t…

This is the first part in a two-part series on complete Calabi-Yau manifolds asymptotic to Riemannian cones at infinity. We begin by proving general existence and uniqueness results. The uniqueness part relaxes the decay condition $O(r^{-n-ε})$ needed in earlier work to $O(r^{-ε})$, relying on some new ideas about harm…

Paper finds surface groups can deform in reductive symmetric spaces.