Local study of foliation deformation cohomology.
problem Understanding deformations of singular foliations.
method Introducing and studying local deformation cohomology.
result Local deformation cohomology for singular foliations and related structures.
Locally connected deformation spaces for 3-manifolds.
problem Locating quasiconformally rigid points in hyperbolic 3-manifolds.
method Proving local connectedness at specific points in the deformation space.
result The deformation space is locally connected at quasiconformally rigid points.
Constructs universal local deformations for curves and differential forms.
problem Local deformations of curves and differential forms under preservation of periods.
method Develops Kuranishi families for pairs of curves and meromorphic 1-forms, focusing on hyperelliptic cases.
result First paper in a series developing a deformation theory for spectral curve data of integrable systems.
Study shows stability of locally conformally balanced condition under modifications but not under small deformations.
problem Stability of locally conformally balanced condition under small deformations and modifications.
method Proved stability under proper modifications and instability under small deformations using examples and Hilbert-Chow map.
result Stability of locally conformally balanced condition under proper modifications and instability under small deformations.
Zermelo deformation preserves geodesics and curvature in Finsler metrics.
problem Behavior of geodesics and curvature in Finsler metrics under Zermelo deformation.
method Zermelo deformation with Killing vector fields.
result Zermelo deformation preserves local symmetry in locally symmetric Finsler metrics.
Study shows deformations of quaternionic Kähler manifolds are locally inhomogeneous.
problem Understanding deformations of quaternionic Kähler manifolds.
method Proved one-loop deformation of quaternionic Kähler manifolds are locally inhomogeneous.
result Full isometry group of one-loop deformations has cohomogeneity one.
In this paper, we study deformations of coisotropic submanifolds in a locally conformal symplectic manifold. Firstly, we derive the equation that governs C∞ deformations of coisotropic submanifolds and define the corresponding C∞-moduli space of coisotropic submanifolds modulo the Hamiltonian isotopies.…
Modified constraint operator for localized deformation with dominant energy condition.
problem Handling localized deformation with initial data sets under the dominant energy condition.
method Introduced a modified constraint operator to absorb metric changes and established local surjectivity theorem.
result Promoted dominant energy condition to strict inequality through compactly supported variations.
Localized deformation of scalar curvature and mean curvature on manifolds.
problem Deforming scalar curvature and mean curvature on compact manifolds with boundary.
method Proving localized surjection of scalar curvature and mean curvature map, handling non-variational linearized problem.
result Localized deformations of scalar curvature and mean curvature on compact manifolds are possible.
Extends Gromov non-squeezing to locally conformally symplectic structures.
problem Generalizing Gromov non-squeezing to new geometric structures.
method Deformation theory applied to locally conformally symplectic structures.
result Proves a new extension of the Gromov non-squeezing phenomenon.
We prove that the deformation space AH(M) of marked hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold M with incompressible boundary is locally connected at minimally parabolic points. Moreover, spaces of Kleinian surface groups are locally connected at quasiconformally rigid points. Similar resu…
The study explores deformations of standard locally homogeneous spaces.
problem Understanding how discrete subgroups can be deformed while preserving proper discontinuity.
method Classification results for standard quotients, including local rigidity, deformation criteria, and Zariski-closure conditions.
result Conditions for local rigidity, deformation into nonstandard quotients, and maximal Zariski-closure of discontinuous groups.
We give an explicit construction of a deformation quantization of the algebra of functions on a Poisson manifolds, based on Kontsevich's local formula. The deformed algebra of functions is realized as the algebra of horizontal sections of a vector bundle with flat connection.
The paper explores how to increase Steklov spectral gaps on manifolds with fixed boundary.
problem Finding ways to increase Steklov spectral gaps on manifolds with fixed boundary.
method Constructing compact manifolds with fixed boundary geometry and applying localized conformal deformations.
result It is possible to make the spectral gap arbitrarily large using localized conformal deformations.
Study on deforming complex manifolds and Higgs bundles.
problem Deforming holomorphic-Higgs pairs on complex manifolds.
method Introduced a DGLA and derived the Maurer-Cartan equation to govern the deformation.
result Proved the local completeness of the Kuranishi family of the deformed holomorphic-Higgs pair.
Study noncommutative deformations of Calabi-Yau threefolds.
problem Understanding the geometry of Calabi-Yau threefolds under noncommutative deformations.
method Analyzing the influence of Poisson structures on quantum moduli spaces.
result The choice of Poisson structure significantly affects the geometry of quantum moduli spaces.
Local deformations of solutions to open PDEs can be extended globally if derivatives are constant along a subset.
problem Extending local deformations to global deformations for solutions to open PDEs.
method Showing that local deformations can be extended globally if derivatives are constant along a closed subset.
result General approximation result by sections with very restrictive local properties on dense open subsets.
Local stability of p-Kähler structures studied.
problem Stability of p-Kähler structures under deformations.
method Natural extension map and power series method.
result Local stability theorem for p-Kähler structures.
Proves conjecture on deformation invariance of big fundamental groups.
problem Stability of big fundamental groups under small deformations.
method Deformation regularity of equivariant pluriharmonic maps and techniques from Shafarevich conjectures.
result Deformation openness of big fundamental groups for varieties with big complex local systems.
Representing 3D shape deformations by linear models in high-dimensional space has many applications in computer vision and medical imaging, such as shape-based interpolation or segmentation. Commonly, using Principal Components Analysis a low-dimensional (affine) subspace of the high-dimensional shape space is determin…
The purpose of this work is to close the local deformation problem of rank two Euclidean submanifolds in codimension two by describing their moduli space of deformations. In the process, we provide an explicit simple representation of these submanifolds, a result of independent interest by its applications. We also det…
The paper discusses q-deformations of the Aomoto complex.
problem Deformation of cochain complexes associated with hyperplane arrangements.
method Replaces entries of coboundary maps with q-analogues and analyzes the resulting structures. result The q-deformation can be a cochain complex under certain conditions and yields local system cohomology groups. New instanton homology for webs counts Tait colorings.
problem Counting Tait colorings of complex webs.
method Introducing a local system of coefficients to deform instanton homology.
result Rank of deformed instanton homology equals number of Tait colorings.
Study shows compact Sasakian manifolds are locally Heisenberg up to deformation.
problem Characterizing compact Sasakian manifolds.
method Analyzing basic Chern classes and using left invariant Sasakian structures.
result Compact Sasakian manifolds are locally isomorphic to the real Heisenberg group.
We provide an infinite family of pared manifolds whose relative deformation spaces of hyperbolic structures on these manifolds are not locally connected. This is a natural extension of the recent result of Bromberg that shows the space of Kleinian punctured torus groups is not locally connected.
Study non-Kahler symplectic manifolds, proving deformation and Torelli theorems.
problem Topology and deformation theory of non-Kahler holomorphically symplectic manifolds.
method Investigation of topology and deformation theory, proving local Torelli theorem and Fujiki formula.
result Holomorphically symplectic deformations of BG-manifolds are unobstructed, and the period map is locally a diffeomorphism.
The paper extends curve deformation methods in Minkowski plane.
problem Studying deformations of curves in the Minkowski plane considering their geometry and singularities.
method Extends methods from [17, 18] to analyze 2-parameter families of curves in Minkowski plane.
result Obtains geometry of deformed curves, including inflections, vertices, and lightlike points.
Study Wilson lines junctions in quantum groups with one-parameter deformations.
problem Understanding local relations of Wilson lines in quantum groups.
method Analyzing junctions of Wilson lines in refined SU(N) Chern-Simons theory and proposing local relations.
result Realization of one-parameter deformations of quantum groups.
DPNs learn pose-invariant object representations.
problem Pose-invariant 2D object recognition.
method Deformable Part Networks (DPNs) as sequences of LDPM units.
result 17-layer DPN outperforms CapsNets and STNs significantly on affNIST.
For any closed surface S of genus g≥2, we show that the deformation space of marked hyperbolic 3-manifolds homotopy equivalent to S, AH(S×I), is not locally connected. This proves a conjecture of Bromberg who recently proved that the space of Kleinian punctured torus groups is not locally connected.…
Researchers glue and deform Calabi-Yau 3-folds, proving local diffeomorphisms.
problem Deforming and gluing asymptotically cylindrical Calabi-Yau 3-folds.
method Developed new proofs for gluing and deformation, extending results to the asymptotically cylindrical case.
result Proved the gluing map is a local diffeomorphism, connecting moduli spaces of Calabi-Yau structures.
Novel approach uses quasi-conformal geometry for OSA classification from cephalometry.
problem Classifying obstructive sleep apnea (OSA) based on craniofacial profiles.
method Quasi-conformal geometry for local deformation analysis of 15 landmark points in lateral cephalograms.
result Proposed model achieves 92.5% testing accuracy.
We consider the deformation of a discontinuous group acting on the Euclidean space by affine transformations. A distinguished feature here is that even a `small' deformation of a discrete subgroup may destroy proper discontinuity of its action. In order to understand the local structure of the deformation space of disc…
Researchers derived heat kernel expansions for non-compact spaces using Witten deformation.
problem Heat kernel expansions on non-compact spaces, especially for Witten Laplacians.
method Introduced parabolic distance and used it to derive asymptotic expansions.
result Derived an asymptotic expansion of trace of heat kernel for small-time t. The paper explores moduli space of heterotic system using two deformation paths.
problem Exploring the moduli space of the heterotic system.
method Considering two dual deformation paths starting from a Kähler solution, one along Bott-Chern cohomology class and the other along Aeppli cohomology class. Using the implicit function theorem to prove local existence of heterotic solutions.
result Established an initial step to construct local moduli coordinates around a Kähler solution.
Discrete model of curve deformation using discrete nonlinear Schrödinger equation.
problem Deformation of discrete space curves.
method Discrete analogue of the local induction equation using the discrete nonlinear Schrödinger equation.
result Explicit formulas for smooth and discrete curves in terms of τ functions of the two-component KP hierarchy.
We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds, more precisely, on Sn×Tm, where Tm is a torus of dimension m≥2 and Sn is a sphere of dimension n≥4. These metrics are not locally homogeneous; in particu…
Study local topology of a function-germ deformation with a one-dimensional critical set.
problem Analyze the local topology of a deformation of a function-germ with a one-dimensional critical set.
method Use the Brasselet number to study the local topology of a deformation of a function-germ.
result Present a new proof of the Lê-Iomdin formula for the Brasselet number.
Study on isometric submanifolds with preserved Gauss map metrics.
problem Investigating isometric immersions with preserved Gauss map metrics.
method Local analysis of isometric immersions and deformations in Euclidean space.
result Local characterization of non-minimal and non-reducible isometric immersions.
Unified treatment of gauge theories and Yang-Mills theory duality.
problem Unified treatment of gauge theories and Yang-Mills theory duality.
method Cohomological localization techniques and Atiyah-Singer index theorem.
result Unified framework and simplified derivations of localization formulas.
The abstract presents power series proofs for local stabilities of Kähler and balanced structures.
problem Local stabilities of Kähler and balanced structures on complex manifolds.
method Power series method applied to a natural map of complex differential forms.
result New local stability theorems for balanced structures and p-Kähler structures.
Study on deformations of LC Spin(7) instantons simplifies the problem.
problem Deformation theory of instantons on locally conformal Spin(7) manifolds.
method Reformulated linearized deformation equations using a t-parameter family of Dirac operators, demonstrating cancellation of torsion terms.
result The deformation space H^1 is governed by Levi-Civita geometry, reducing the problem to a torsion-free setting.
The paper studies deformations and confluences of singularities in meromorphic connections and quadratic differentials.
problem Understanding singularities and deformations in meromorphic connections and quadratic differentials.
method Local formal invariants and jets of meromorphic quadratic differentials, universal isomonodromic deformation, unfolded Stokes phenomenon, horizontal and vertical foliations.
result Establishes a correspondence between local formal invariants and jets of meromorphic quadratic differentials, describing parameter spaces and moduli spaces.
Study on complex manifolds introduces a new deformation of the Yamabe problem.
problem Yamabe-type problems on compact Hermitian manifolds.
method Introducing a one-parameter Hermitian deformation of the Yamabe problem, defined by adding natural torsion terms to the Riemannian scalar curvature.
result Analysis of criteria for the existence of solutions and discussion of examples.
Flow deforms locally convex curves to curves of constant k-order width.
problem Evolve locally convex curves to curves of constant k-order width.
method Introduced a nonlocal curvature flow to evolve locally convex curves in the plane.
result The flow converges to a smooth, locally convex curve of constant k-order width as time goes to infinity.
Kuranishi's proof of complex deformation theory revisited
problem Existence of complex deformations on compact complex manifolds
method Hamilton-Nash-Moser implicit function theorem
result Revisits classical proof with modern tools
New principle for supersymmetric localization on Lie groups.
problem Computing supertrace of non-supersymmetric observables.
method Invariant supersymmetric deformations and fermionic zero modes.
result Path integral localizes to periodic orbits.
Study gluing and deformations of special Lagrangian submanifolds.
problem Deforming special Lagrangian submanifolds in Calabi-Yau manifolds.
method Proves well-defined gluing map and local diffeomorphism for deformations.
result Gluing map defines local diffeomorphism between deformations.