Invariants found for tau-symmetric bihamiltonian systems.
problem Understanding symmetries in bihamiltonian systems.
method Proof of infinite Virasoro symmetries for tau-symmetric bihamiltonian deformations.
result Infinite set of Virasoro symmetries for tau-symmetric bihamiltonian systems.
Linearizes Virasoro symmetries for semisimple Frobenius manifolds.
problem Linearizing Virasoro symmetries for semisimple Frobenius manifolds.
method Proving the existence of an infinite family of linearizable Virasoro symmetries under specific conditions.
result The Dubrovin-Zhang hierarchy associated with semisimple Frobenius manifolds has a bihamiltonian structure that can be represented by differential polynomials.
A mathematical model describes deforming manifolds with precise vectors and fields.
problem Modeling and describing the deformation of complex manifolds in practical applications.
method Proposes a modified differential dynamic model with constraints on spatial and temporal continuity, presenting deforming vector and field.
result Demonstrates the effectiveness of an autonomous deforming field in data dimension reduction tasks.
Study YB operators and their deformations, finding integrable and nontrivial cases.
problem Understanding deformations of Yang-Baxter operators and their integrability.
method Relating deformations to Lie algebra deformations, analyzing cohomology groups.
result Existence of integrable YB deformations and nontrivial cases not arising from SD deformations.
Smooth deformation of Moishezon manifolds preserves their Moishezon property.
problem Preserving Moishezon property under smooth deformation.
method Smooth deformation over a unit disk in C.
result Deformation limit of Moishezon manifolds is Moishezon.
In this paper, we study deformations of holomorphic Poisson maps which extend Horikawa's series of papers on deformations of holomorphic maps in the context of holomorphic Poisson deformations. In appendices, we present deformations of Poisson morphisms in the language of functors of Artin rings which is the algebraic …
In this paper we study the deformation theory of submanifolds characterized by a system of differential forms and provide a criterion for deformations of such submanifolds to be unobstructed. We apply this deformation theory to special Legendrian submanifolds in Sasaki-Einstein manifolds. In general, special Legendrian…
Study on deformations of Lie groupoid morphisms and their properties.
problem Understanding the deformation theory of Lie groupoid morphisms.
method Established deformation theory, cohomology, and properties of morphisms.
result Invariance and stability properties of morphisms, Morita invariance of cohomology, and simultaneous deformations.
Study canonical deformations of complex forms and their cohomology properties.
problem Understanding canonical deformations and cohomology of complex manifolds.
method Analyzes canonical Aeppli deformations and their relations to deformed cohomology.
result Proves the jumping formula for deformed Aeppli cohomology and constant dimension conditions.
In this paper, we study deformations of compact holomorphic Poisson submanifolds which extend Kodaira's series of papers on semi-regularity (deformations of compact complex submanifolds of codimension 1), deformations of compact complex submanifolds of arbitrary codimensions, and stability of compact complex submanifol…
The L∞-algebra is an algebraic structure suitable for describing deformation problems. In this paper we construct one L∞-algebra, which turns out to be a differential graded Lie algebra, to control the deformations of Lie algebroids and a second one to control the deformations of Lie subalgebroids. We a…
Study on deformations of holomorphic Cartan geometries, focusing on flat cases.
problem Deformation of holomorphic Cartan geometries on complex manifolds.
method Computing infinitesimal deformations and analyzing the forgetful map.
result The forgetful map from infinitesimal deformations of a flat holomorphic Cartan geometry to the underlying flat principal bundle is an isomorphism.
Study infinitesimal deformations of Lie algebroid pairs.
problem Infinitesimal deformations of Lie algebroid pairs.
method Investigate isomorphism classes of infinitesimal deformations of (L,A) modulo automorphisms from exponentials of derivations of L and those from the exponentials of inner derivations of L. result Find the associated governing L∞-algebras in the sense of extended deformation theory. We study infinitesimal conformal deformations of a triangulated surface in Euclidean space and investigate the change in its extrinsic geometry. A deformation of vertices is conformal if it preserves length cross-ratios. On one hand, conformal deformations generalize deformations preserving edge lengths. On the other h…
The paper studies deformations of Filippov algebroids using cohomology and DGLA.
problem Deformations of Filippov algebroids.
method Defined a DGLA for Filippov algebroids and used low-dimensional cohomology to discuss deformations. Characterized trivial deformations using Nijenhuis operators and defined finite order deformations.
result Characterized trivial deformations of Filippov algebroids using Nijenhuis operators.
First non-trivial examples of deformed G_2-instantons, distinguishing nearly parallel G_2-structures.
problem Distinguishing between nearly parallel G_2-structures and isometric G_2-structures.
method Provided first non-trivial examples of deformed G_2-instantons and studied their deformation theory.
result Found non-trivial deformed G_2-instantons with obstructed deformation theory and moduli spaces of different dimensions.
New spherical curve deformations solve a conjecture.
problem Solving the Östlund Conjecture for spherical curves.
method Introducing a new type of deformation (β) and proving equivalence under specific deformations.
result Equivalence of spherical curves under specific deformations.
DeformRS certifies deep networks against various input deformations.
problem Vulnerability of deep networks to input deformations.
method Randomized smoothing reformulation for general deformations.
result Certifies rich deformations including translations, rotations, scaling, and affine.
Study deformations of Calabi-Yau foliations using Kuranishi spaces.
problem Deforming Calabi-Yau foliations and understanding their properties.
method Analysis of three types of deformations (unfoldings, holomorphic, transversally holomorphic) using Kuranishi spaces.
result Smoothness of Kf and product structure of Kh. Study on bending deformations in hyperbolic manifolds, generalizing Johnson and Millson's work.
problem Understanding infinitesimal deformations in branched bending complexes.
method Defining branched bending deformations, giving lower bounds, and constructing examples.
result Lower bounds on the dimension of deformation spaces and examples of specific deformations.
The paper studies deformations of cohesive modules on complex manifolds.
problem Deformation theory of cohesive modules on compact complex manifolds.
method Development of Kuranishi maps and obstructions for deformations of cohesive modules.
result Generalization of deformation theory for holomorphic vector bundles and coherent sheaves.
We consider some natural infinitesimal Einstein deformations on Sasakian and 3-Sasakian manifolds. Some of these are infinitesimal deformations of Killing spinors and further some integrate to actual Killing spinor deformations. In particular, on 3-Sasakian 7 manifolds these yield infinitesimal Einstein deformations pr…
Computes spectral Einstein functional for Witten deformation on even-dimensional spin manifolds.
problem Calculating the spectral Einstein functional for a specific deformation.
method Computes the spectral Einstein functional for the Witten deformation on even-dimensional spin manifolds.
result Computed the spectral Einstein functional for the Witten deformation on even-dimensional spin manifolds.
Study how pairs of 1D foliations can be deformed into contact structures.
problem Understanding deformations of pairs of 1D foliations.
method Linear deformations of pairs of codimension one foliations into contact pairs.
result Main result provides applications and insights into foliation deformations.
Study geometric properties of S1 singularities and their deformations.
problem Understanding differential geometric properties of S1 singularities and deformations.
method Representing deformation using diffeomorphisms and isometries, studying geometric properties.
result Differential geometric properties of S1 singularities and Whitney umbrellas in deformations.
Introducing the deformation theory of holomorphic Cartan geometries, we compute infinitesimal automorphisms and infinitesimal deformations. We also prove the existence of a semi-universal deformation of a holomorphic Cartan geometry.
Develops deformation theory for symplectic foliations using L∞-algebras.
problem Deformation of symplectic foliations.
method Uses L∞-algebras to control deformation problems. result Establishes a correspondence between small deformations and Maurer-Cartan elements of L∞-algebra. Study on deformation cohomology for braided commutative structures.
problem Classifying and understanding deformations of braided commutative algebras.
method Extending Yang-Baxter Hochschild cohomology to braided commutative deformations.
result Classifies infinitesimal deformations of braided algebras that are braided commutative.
Study on Einstein deformations of negative Kähler Einstein metrics.
problem Understanding Einstein deformations of Kähler Einstein metrics.
method Relate second order Einstein deformation theory to complex geometry, gauge normalise, and use Taylor expansion.
result Taylor expansion to order two of an Einstein deformation is determined by h12 and the divergence of the Kodaira-Spencer bracket. 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.…
Maps geometric deformations to algebraic classes in Lie groupoids and algebroids.
problem Deformation theory of Lie groupoids and algebroids.
method Defining a morphism between deformation complexes and Hochschild complexes, applying to adiabatic groupoids.
result Induced van Est map from geometric to algebraic deformation cohomology.
We consider the stability of Sasaki-extremal metrics under deformations of the complex structure on the Reeb foliation. Given such a deformation preserving the action of a compact subgroup of the automorphism group of a Sasaki-extremal structure, a sufficient condition is given involving the nondegeneracy of the relati…
Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define motions and conformal motions together with deformational decomposition of manifol…
Study strip deformations of hyperbolic polygons with decorated vertices.
problem Understanding deformations of hyperbolic polygons with decorated vertices.
method Analyzing strip deformations of ideal hyperbolic polygons with horoballs.
result Arc complexes parameterize uniformly lengthening deformations.
In this thesis, we study deformations of compact holomorphic Poisson manifolds and algebraic Poisson schemes in the framework of Kodaira-Spencer's analytic deformation theory and Grothendieck's algebraic deformation theory.
We extend to the conformal realm the concept of genuine deformations of submanifolds, introduced by Dajczer and the first author for the isometric case. Analogously to that case, we call a conformal deformation of a submanifold Mn genuine if no open subset of Mn can be included as a submanifold of a higher dimens…
We consider deformations of G-structures via the right action on the frame bundle in a base-point-dependent manner. We investigate which of these deformations again lead to G-structures and in which cases the original and the deformed G-structures define the same instantons. Further, we construct a bijection from conne…
Study deformations of compact Kähler hyperbolic manifolds.
problem Investigate the deformation openness of Kähler hyperbolicity.
method Propose modified versions of Kähler hyperbolicity as a tool.
result Provide a first step towards understanding deformations.
Deformations of compact Riemann surfaces are considered using a Čech cohomology sliding overlaps approach. Cocycles are calculated for conformal cutting and regluing deformations at zeros of Abelian differentials. A second order deformation expansion is presented for the Riemann period matrix. A complete deformation ex…
Study projective deformations of hyperbolic 3-orbifolds with turnover ends.
problem Deformations of hyperbolic 3-orbifolds with turnover ends in projective geometry.
method Projective deformations of hyperbolic 3-orbifolds with turnover ends, focusing on totally geodesic generalized cusps.
result Turnover funnels remain totally geodesic and the deformed projective 3-orbifold remains properly convex.
Minimal surfaces can be transformed into others with unchanged bending content.
problem Understanding the deformation properties of minimal surfaces.
method Refined polar decomposition theorem to identify bending-neutral deformations.
result Every minimal surface can be transformed into another by a bending-neutral deformation.
The Epstein deformation space parameterizes marked rational maps with prescribed combinatorial and dynamical structure. For the family of quadratic rational maps with a periodic critical cycle of order 4 and an extra critical point not lying in this cycle, S. Koch and I recently showed that the deformation space has in…
In this paper, we use the parametrised strict deformation quantization of C*-bundles obtained in a previous paper, and give more examples and applications of this theory. In particular, it is used here to classify H_3-twisted noncommutative torus bundles over a locally compact space. This is extended to the case of gen…
Study second-order obstruction to nearly G2 structure deformations.
problem Proper nearly G2 structure rigidity on Aloff-Wallach space. method Second-order obstruction analysis, building on Alexandrov and Semmelmann work.
result Proves rigidity for nearly G2 structure on N(1,1). Study deforms Hermitian metrics with positive curvature.
problem Deforming Hermitian metrics with positive curvature.
method Adapted conformal perturbation method to Hermitian setting.
result Hermitian metrics with quasi-positive curvature can be deformed to positive curvature.
We generalize results of Lee, Gornik and Wu on the structure of deformed colored sl(N) link homologies to the case of non-generic deformations. To this end, we use foam technology to give a completely combinatorial construction of Wu's deformed colored sl(N) link homologies. By studying the underlying deformed higher r…
Completes the classification of Moebius deformable hypersurfaces for dimensions 5 and above.
problem Missing examples in the classification of Moebius deformable hypersurfaces for dimensions 5 and above.
method Investigates the class of Moebius deformable hypersurfaces and completes the classification for dimensions 5 and above.
result Completes the classification of Moebius deformable hypersurfaces for dimensions 5 and above.
This research classifies deformations of Yang-Baxter operators using cohomology of n-Lie algebras.
problem Classifying deformations of Yang-Baxter operators via cohomology of n-Lie algebras. method Introducing a cohomology theory for n-ary self-distributive objects, showing natural injections and isomorphisms, and constructing deformation theories. result The self-distributive deformations classify the Yang-Baxter operator deformations, with nontrivial examples provided.