arXiv research

Smooth deformation of Moishezon manifolds preserves their Moishezon property.

Maps geometric deformations to algebraic classes in Lie groupoids and algebroids.

Anosov subgroups' deformations affect limit cones and growth indicators continuously.

Paper introduces a new metric for deforming surfaces with parabolics.

Wiatowski and Bölcskei, 2015, proved that deformation stability and vertical translation invariance of deep convolutional neural network-based feature extractors are guaranteed by the network structure per se rather than the specific convolution kernels and non-linearities. While the translation invariance result appli…

We construct a geometric structure on deformed supermanifolds as a certain subalgebra of the vector fields. In the classical limit we obtain a decoupling of the infinitesimal odd and even transformations, whereas in the semiclassical limit the result is a representation of the supersymmetry algebra. In the case of mass…

We give a brief overview of the current state of the study of the deformation theory of Kleinian groups. The topics covered include the definition of the deformation space of a Kleinian group and of several important subspaces; a discussion of the parametrization by topological data of the components of the closure of …

Formula connects analytic torsion forms of fibration and its pieces.

The paper proves conditions for solutions of $J$-equation and deformed Hermitian-Yang-Mills equation on holomorphic submersions.

The paper studies limits of flows on Kähler surfaces, proving convergence to solutions of equations.

Deformation estimation of elastic object assuming an internal organ is important for the computer navigation of surgery. The aim of this study is to estimate the deformation of an entire three-dimensional elastic object using displacement information of very few observation points. A learning approach with a neural net…

Study on Einstein deformations and desingularizations, finding some 4-orbifolds cannot be limits of smooth metrics.

Study of deformations of Virasoro symmetries using variational bihamiltonian cohomology.

We present a simpler proof for the existence of adiabatic limits. Moreover, we added a new section where the adiabatic process is reversed and in some nondegenerate cases we deform the adiabatic limits to genuine irreducible solutions of the SW equations.

We study proper, isometric actions of nonsolvable discrete groups Gamma on the 3-dimensional Minkowski space R^{2,1} as limits of actions on the 3-dimensional anti-de Sitter space AdS^3. To each such action is associated a deformation of a hyperbolic surface group Gamma_0 inside O(2,1). When Gamma_0 is convex cocompact…

We introduce a new kind of groupoid--a pseudo étale groupoid, which provides many interesting examples of noncommutative Poisson algebras as defined by Block, Getzler, and Xu. Following the idea that symplectic and Poisson geometries are the semiclassical limits of the corresponding quantum geometries, we quantize thes…

The paper derives Gauss-Bonnet theorems for deformed connections in affine and rigid motions groups.

Study earthquake deformations on a once-punctured torus.

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

This research connects Higgs bundles to projective structures via conformal limits.

Deformed holomorphic Chern-Simons theory yields new instantons.

The note proves a metric equivalence for stable bundles on surfaces.

The geometry of the Heisenberg group acting on the plane arises naturally in geometric topology as a degeneration of the familiar spaces $\mathbb{S}^2,\mathbb{H}^2$ and $\mathbb{E}^2$ via conjugacy limit as defined by Cooper, Danciger, and Wienhard. This paper considers the deformation and regeneration of Heisenberg st…

Study Kähler-Einstein edge metrics on Hirzebruch surfaces, verifying a conjecture and finding a rigid singularity.

Let $(N,g_{0})$ be a Kahler-Einstein surface with the first Chern class negative and assume that there exists a branched Lagrangian minimal surfaces with respect to the metric $g_{0}$. We show that when the Kahler-Einstein metric is changed in the same component (i.e. the complex structure is changed), the Lagrangian m…

The paper analyzes thin-shell limits for viscous operators on Riemannian hypersurfaces.

We compute the central invariants of the bihamiltonian structures of the constrained KP hierarchies, and show that these integrable hierarchies are topological deformations of their hydrodynamic limits.

In this paper we describe the cohomogeneity one special Lagrangian 3-folds in the cotangent bundle of the 3-sphere, also known in the physics literature as a deformed conifold. Our main result gives a global foliation of the deformed conifold by T^2-invariant special Lagrangian 3-folds, where the generic leaf is topolo…

We study sequences of conformal deformations of a smooth closed Riemannian manifold of dimension $n$, assuming uniform volume bounds and $L^{n/2}$ bounds on their scalar curvatures. Singularities may appear in the limit. Nevertheless, we show that under such bounds the underlying metric spaces are pre-compact in the Gr…

We review the relations between compact complex manifolds carrying various types of Hermitian metrics (Kähler, balanced or {\it strongly Gauduchon}) and those satisfying the $\partial\bar\partial$-lemma or the degeneration at $E_1$ of the Frölicher spectral sequence, as well as the behaviour of these properties under h…

We introduce and compute a 2-parameter family deformation of the A-polynomial that encodes the color dependence of the superpolynomial and that, in suitable limits, reduces to various deformations of the A-polynomial studied in the literature. These special limits include the t-deformation which leads to the "refined A…

Develops a Riemannian archetypal analysis for interpretable non-linear data.

CycleMorph improves image registration by preserving topology with cycle consistency.

The article develops deformation theory for ACyl associative submanifolds in ACyl G2-manifolds.

The paper studies neural networks with wide layers and finds a deformed semicircle law.

New framework reveals limits of flexible, periodic thin surfaces.

Traditional vision-based hand gesture recognition systems is limited under dark circumstances. In this paper, we build a hand gesture recognition system based on microwave transceiver and deep learning algorithm. A Doppler radar sensor with dual receiving channels at 5.8GHz is used to acquire a big database of hand ges…

We introduce a natural map from the space of pure-type complex differential forms on a complex manifold to the corresponding one on the infinitesimal deformations of this complex manifold. By use of this map, we generalize an extension formula in a recent work of K. Liu, X. Yang and the first author. As direct corollar…

Consider a geometrically finite Kleinian group $G$ without parabolic or elliptic elements, with its Kleinian manifold $M=(\H^3\cup Ω_G)/G$. Suppose that for each boundary component of $M$, either a maximal and connected measured lamination in the Masur domain or a marked conformal structure is given. In this setting, w…

Along cuspidal edge singularities on a given surface in Euclidean 3-space, which can be parametrized by a regular space curve, a unit normal vector field $ν$ is well-defined as a smooth vector field of the surface. A cuspidal edge singular point is called generic if the osculating plane of the cuspidal edge (as a regul…

For a complex flat vector bundle over a fibered manifold, we consider the 1-parameter family of certain deformed sub-signature operators introduced by Ma-Zhang. We compute the adiabatic limit of the Bismut-Freed connection associated to this family and show that the Bismut-Lott analytic torsion form shows up naturally …

We propose a generalization of quantization as a categorical way. For a fixed Poisson algebra quantization categories are defined as subcategories of R-module category with the structure of classical limits. We construct the generalized quantization categories including matrix regularization, strict deformation quantiz…

Study extends Hausdorff dimension Hessian results to new hyperconvex representations.

This thesis is devoted to various questions connected with duality. It is composed of two parts. The first part discusses some aspects of timelike T-duality. We explore the possibility of compactification of supergravity theories with various signatures (low energy limit of $M$-theories which are dual under timelike T-…

Study on eigenvalue distribution of correlated time series deforming the semi-circle law.

We classify simply connected compact Sasaki manifolds of dimension $2n+1$ with positive transverse bisectional curvature. In particular, the Kähler cone corresponding to such manifolds must be bi-holomorphic to $\C^{n+1}\backslash \{0\}$. As an application we recover the Mori-Siu-Yau theorem on the Frankel conjecture a…

Study k-positive surface group representations and their degenerations.

The paper extends Bour's theorem to helicoidal surfaces with singularities.