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.
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.
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.
The thesis explores integrable systems and rigidity in PDEs with symmetry.
problem Understanding the deformation theory and rigidity of PDEs with symmetry.
method The approach involves studying completely integrable systems, their equivalence relations, and the deformation theory of PDEs with pseudogroups of symmetries.
result A solution is rigid if its deformation cohomology vanishes and certain estimates hold.
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.
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.…
The thesis explores dualities and gaugings in supergravity theories.
problem Exploring dualities and gaugings in supergravity theories.
method Analyzing the space of local deformations and the BV-BRST deformation of scalar-vector coupled Lagrangians.
result Only Yang-Mills type deformations are possible for a large class of theories.
The paper studies deformations of Calabi-Yau manifolds using Gauduchon metrics.
problem Deformations of Calabi-Yau manifolds under co-polarised conditions.
method Analyzes local deformations of Calabi-Yau ∂∂ˉ-manifolds using Gauduchon metrics and constructs a new hp-HS form. result Proves the p-SKT h-∂∂ˉ-property is deformation open. We investigate the local deformation space of 3-dimensional cone-manifold structures of constant curvature κ∈{−1,0,1} and cone-angles ≤π. Under this assumption on the cone-angles the singular locus will be a trivalent graph. In the hyperbolic and the spherical case our main result is a vanishing theorem fo…
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…
Paper finds surface groups can deform in reductive symmetric spaces.
problem Finding deformations of discontinuous groups in reductive symmetric spaces.
method Analyzing Zariski dense surface subgroups and their deformations.
result Surface groups of high genus can deform in reductive symmetric spaces.
Introduces Witten deformation and its applications in topology.
problem Analyzing and applying Witten deformation in topology.
method Deformation of Dirac operators and analytic proofs.
result Analytic proofs of Poincaré-Hopf index theorem, Real Morse inequalities, Thom-Smale complex quasi-isomorphism, and Atiyah vanishing theorem.
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 $\T_g$…
In this paper we prove that every Riemannian metric on a locally conformally flat manifold with umbilic boundary can be conformally deformed to a scalar flat metric having constant mean curvature. This result can be seen as a generalization to higher dimensions of the well known Riemann mapping Theorem in the plane.
Second part of Q-curvature research focusing on volume comparison.
problem Volume control and rigidity of Q-curvature.
method Volume comparison and local rigidity analysis.
result Volume comparison theorem for metrics close to strictly stable positive Einstein metrics.
Study examines deformations of Kerr-(A)dS near horizon geometry.
problem Analyzing deformations of Kerr-(A)dS near horizon geometry.
method Two-part proof: elimination of Fourier modes and analyticity argument.
result No odd Fourier modes found for linear perturbations.
Paper discusses star products and Kähler metrics, linking deformation quantization and constant curvature metrics.
problem Existence of Kähler metrics with constant scalar curvature.
method Analyzes Fedosov and Berezin-Toeplitz star products, and studies K-stability conditions.
result Formulates a cohomology formula for K-stability conditions on Kähler metrics.
In the first part we define a "BTZ" black hole in anti de Sitter space in any dimension by defining as "singular" the closed orbits of the Iwasawa component of SO(2,n). In the second part, a strict quantization of the black hole by action of group is performed and its Dirac operator is computed. We introduce, in the ap…
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.
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…
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.
The paper develops finite knot theory using ropelength-filtered Reidemeister graphs.
problem Understanding knot types in bounded ropelength sublevel spaces.
method Study thick representatives in bounded ropelength sublevel spaces through lifted Reidemeister graphs.
result Define characteristic Reidemeister patterns and finite recognition length.
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.
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.
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.
The paper analyzes Kähler-Ricci flow near Kähler-Ricci solitons under complex structure deformation.
problem Behavior of Kähler-Ricci flow near Kähler-Ricci solitons under complex structure deformation.
method Established Lojasiewicz's type inequality for Perelman's entropy and proved convergence of Kähler-Ricci flow.
result Solved Yau-Tian-Donaldson conjecture and showed the kernel Z corresponds to local moduli space of modified K-semistable Fano manifolds. 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…
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.…
Affine deformations of convex cones yield special spacetime structures.
problem Deforming divisible convex cones in affine spaces.
method Analyzing the maximal convex domains and quotient structures.
result Quotients of affine actions are MGHCC affine spacetimes.
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.
Geometric interpretation of 2d-4d wall-crossing formulas.
problem Understanding wall-crossing phenomena in coupled 2d-4d systems.
method Deformation theory of holomorphic pairs and relation to scattering diagrams.
result Geometric interpretation of 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…
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…
New method tackles rugged optimization landscapes in contact-rich scenarios.
problem Optimization challenges in dynamic environments with deformable objects.
method Combines Bayesian optimization with semi-local 'leaps' for global search.
result Outperforms gradient-based and gradient-free baselines in simulation and real robot experiments.
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.
Margulis space-times with parabolic holonomy elements are stable under sufficiently small deformations.
problem Stability of Margulis space-times with parabolic holonomy elements
method Combining compactification and partial generalization of earlier work
result Openness result on the number of conjugacy classes of parabolic elements under deformation
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…
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.
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. 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.
The paper proves the regularity and compactness of stable CMC integral varifolds in codimension 1.
problem Stable CMC integral varifolds of codimension 1.
method Structural conditions and variational hypotheses.
result The support of the varifold is an immersed constant-mean-curvature (CMC) hypersurface under given conditions.
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.