Proves a theorem for 3D Poincaré duality pairs.
problem No specific problem stated; focuses on proving a theorem.
method Analogous to Johannson's theorem for PD3 pairs.
result Proves a theorem for 3D Poincaré duality pairs.
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48 results for “Deformation theorem”
Abstract: Lipschitz homeomorphisms are deformed using Perelman's methods.
problem Deformation of Lipschitz homeomorphisms
method Lipschitz analogues of Siebenmann's and Perelman's homeomorphism theory
result Lipschitz stability theorem and gluing theorem
The paper proves formulas and theorems for J-Witten deformation on specific manifolds.
problem Analyzing J-Witten deformation on specific types of manifolds.
method Obtained a Lichnerowicz type formula and proved Kastler-Kalau-Walze type theorems.
result Proved the Kastler-Kalau-Walze type theorems for J-Witten deformation on 4D and 6D almost product spin manifolds.
The paper studies deformations of Lagrangian submanifolds using algebraic tools.
problem Deformation theory of Lagrangian submanifolds in symplectic geometry.
method Graded versions of the Darboux Theorem and Weinstein's Lagrangian tubular neighbourhood Theorem, attaching an -algebra to each submanifold.
result Controls the deformation theory of Lagrangian -submanifolds using an -algebra.
Proof of theorem for 7D manifolds with boundary using Witten deformation.
problem Proving a theorem for 7-dimensional manifolds with boundary.
method Brute-force proof using Witten deformation.
result Proof of Kastler-Kalau-Walze type theorem for 7D manifolds with boundary.
New theorem connects minimal and maximal surfaces, affecting graphness.
problem Understanding graphness of minimal surfaces in different spaces.
method Introducing a new deformation family and proving Krust-type theorems.
result Graphness of minimal surfaces in isotropic 3-space affects deformed surfaces.
Generalizes Frobenius theorem to quasiconformal deformations.
problem Integrability of plane fields generated by quasiconformal deformations.
method Generalization of classical Frobenius theorem to plane fields.
result A.e. involutive plane fields are integrable.
The paper derives Gauss-Bonnet theorems for deformed connections in affine and rigid motions groups.
problem Computing curvature and geodesic curvature for surfaces and curves in affine and rigid motions groups.
method Defined deformed Schouten-Van Kampen connections, computed Gaussian curvature limits, and signed geodesic curvature.
result Derived Gauss-Bonnet theorems for deformed connections in affine and rigid motions groups.
In this paper we obtain a stability theorem of generalized Kahler structures with one pure spinor under small deformations of generalized complex structures. (This is analogous to the stability theorem of Kahler manifolds by Kodaira-Spencer.) We apply the stability theorem to a class of compact Kahler manifolds which a…
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
Introduces new holomorphic contact structures and proves unobstructedness theorems.
problem Generalizing classical holomorphic contact and symplectic structures.
method Introducing new classes of holomorphic -contact and -symplectic manifolds, observing their properties, and proving structure and unobstructedness theorems.
result Generalizes classical results on small deformations of complex structures.
On Deformation Space Analogies between Kleinian Reflection Groups and Antiholomorphic Rational Mapsmath.DS
This paper shows similarities in deformation spaces of Kleinian groups and anti-holomorphic maps.
problem Comparing deformation spaces of Kleinian reflection groups and anti-holomorphic rational maps.
method Established an analogue of Thurston's compactness theorem for critically fixed anti-rational maps and characterized deformation space interactions.
result Deformation spaces of Kleinian reflection groups and anti-holomorphic rational maps share striking similarities.
Degenerate twistor deformations of Kähler manifolds are also Kähler.
problem Understanding the Kähler structure of degenerate twistor deformations.
method Using positive currents, Hahn–Banach theorem, and Huybrechts's theorem.
result Degenerate twistor deformations of compact holomorphically symplectic Kähler manifolds are Kähler.
In \cite{Goto}, Ryushi Goto has constructed the deformation space for a manifold equipped with a collection of closed differential forms and showed that in some important cases (Calabi-Yau, - and -structures) this deformation space is smooth. This result unifies the classical Bogomolov-Tian-Todorov and Jo…
Proves super-version of index theorem from algebraic cobordism invariants.
problem Cobordism invariants in supersymmetric quantum mechanics.
method Trace methods for deformation quantization.
result Recovery of cobordism invariant using trace methods.
New equations reveal moduli space rigidity in geometric deformations.
problem Understanding moduli space rigidity in geometric deformations.
method Coupled Hitchin-He equations, Lax pair, nonlinear embedding.
result Moduli space is analytically isomorphic to the classical case for small deformations.
Study new involutivity theorems for Poisson quasi-Nijenhuis manifolds.
problem Understanding involutivity in Poisson quasi-Nijenhuis geometry.
method Present new versions of deformation and involutivity theorems under specific factorization hypotheses.
result New versions of involutivity theorems for Poisson quasi-Nijenhuis manifolds.
Study metric perturbations to make degenerate harmonic forms non-degenerate.
problem Dealing with degenerate harmonic 1-forms in Riemannian geometry.
method Combining analysis of local expansions with Nash-Moser implicit function theorem.
result Proves deformation to nearby non-degenerate Z/2-harmonic 1-forms.
We extend the formality theorem of M. Kontsevich from deformations of the structure sheaf on a manifold to deformations of gerbes.
Study instantons on asymptotically conical Spin(7)-manifolds, identifying deformation spaces.
problem Deformation theory of instantons on specific Spin(7)-manifolds.
method Relating deformation complex to spinors, identifying kernel of twisted negative Dirac operator.
result Virtual dimension of moduli space calculated using index theorem and Dirac operator spectrum.
Global homotopies upgrade classical map in differential geometry.
problem Upgrade classical Hochschild-Kostant-Rosenberg map to a deformation retract.
method Combining symbol calculus and coalgebraic van Est theorem.
result Develop deformation retracts in various settings.
Researchers find explicit Bäcklund transforms for specific quadrics.
problem Isometric deformations of diagonal higher dimensional quadrics without center.
method Explicitly found Bäcklund transforms using the Bianchi Permutability Theorem and 3-moving Möbius configuration.
result Explicit solutions can be iterated with arbitrary constants.
We study a notion of deformation for simplicial trees with group actions (G-trees). Here G is a fixed, arbitrary group. Two G-trees are related by a deformation if there is a finite sequence of collapse and expansion moves joining them. We show that this relation on the set of G-trees has several characterizations, in …
In this paper, we define a concept of a family of compact holomorphic Poisson manifolds on the basis of Kodaira-Spencer's deformation theory and deduce the integrability condition. We prove an analogue of their `Theorem of existence for complex analytic structures' under some analytic assumption, and establish an analo…
Witten deformation connects manifold spectra to Morse functions.
problem Understanding spectral properties of Riemannian manifolds.
method Rellich-Kato theorem applied to Witten deformation.
result Relates spectral package to Morse complex and harmonic oscillators.
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 .
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.
A hypersurface without umbilics in the n+1 dimensional Euclidean space is known to be determined by the Moebius metric and the Moebius second fundamental form up to a Moebius transformation when n>2. In this paper we consider Moebius rigidity for hypersurfaces and deformations of a hypersurface preserving the Moebius m…
This is a simple reading report of professor Weiping Zhang's lectures. In this article we will mainly introduce the basic ideas of Witten deformation, which were first introduced by Edward Witten on, and some applications of it. The first part of this article mainly focuses on deformation of Dirac operators and some im…
We prove a Darboux theorem for formal deformations of Hamiltonian operators of hydrodynamic type (Dubrovin-Novikov). Not all deformations are equivalent to the original operator: there is a moduli 2-stack of normal forms. The paper utilizes three main concepts: 1) dg Lie algebras concentrated in degrees [-1,\infty) suc…
The paper examines deformations of pseudoholomorphic curves in a nearly Kähler sphere.
problem Investigating rigidity and deformability of pseudoholomorphic curves in .
method Analyzing moduli space of minimal surfaces isometric to pseudoholomorphic curves.
result Describes the moduli space of noncongruent minimal surfaces isometric to pseudoholomorphic curves.
Lectures on Symplectic Geometry, Poisson Geometry, Deformation Quantization and Quantum Field Theorymath-ph
Lectures on symplectic and Poisson geometry, quantization, and quantum field theory.
problem Exploring symplectic and Poisson structures and their applications in quantum field theory.
method Introduction to differential geometry, symplectic geometry, Poisson geometry, and deformation quantization.
result Detailed understanding of symplectic and Poisson structures and their quantization.
Proves spacetime positive mass theorem with corners.
problem Proving a positive mass theorem for spacetime with corners.
method Deformation theorem with corner conditions, asymptotically flat initial data.
result Exterior end satisfies in every dimension .
We construct a Laplace isospectral deformation of metrics on an orbifold quotient of a nilmanifold. Each orbifold in the deformation contains singular points with order two isotropy. Isospectrality is obtained by modifying a generalization of Sunada's Theorem due to DeTurck and Gordon.
There is an error in the proof of Theorem 1.1 that invalidates proofs of other theorems. Theorem 1.5 is unaffected.
Homotopy operators help describe structures in equivariant deformation problems.
problem Equivariant deformation problems in algebraic structures.
method Use homotopy operators for an -algebra associated with the problem.
result Smooth parametrization of the space of structures around a given one.
Study finds how periodic surfaces can bend without stretching.
problem Understanding isometric deformations of periodic surfaces.
method Characterization of isometric deformations using a constraint derived from Gauss theorem.
result Relates surface stretching to bending and twisting.
The paper extends Bour's theorem to helicoidal surfaces with singularities.
problem Proving non-trivial isometric deformations for cuspidal edges under helicoidal motion.
method Generalizing Bour's theorem techniques, proving deformations for generic cuspidal edges.
result Geometric invariants are extrinsic for cuspidal edges under helicoidal motion.
Developing deformation theory for Calabi-Yau 3-folds with boundary.
problem Dealing with Calabi-Yau threefolds on manifolds with boundary.
method Deformation theory and local Torelli Theorem for compact manifolds.
result An analogue of Hitchin's local Torelli Theorem for Calabi-Yau 3-folds with boundary, modulo a finite dimensional obstruction space.
In these notes we give a shortened and more direct proof of Goto's generalized Kaehler stability theorem stating that if (J_1,J_2) is a generalized kaehler structure for which J_2 is determined by a nowhere vanishing closed form, then small deformations of J_1 can be coupled with small deformations of J_2 so that the p…
Paper extends noncompact Llarull's theorem to manifolds with boundary.
problem Finding upper bounds for scalar curvature infimum in noncompact manifolds.
method Using deformed Dirac operators to relax boundary conditions.
result Upper bound for scalar curvature infimum in terms of Laplacian spectrum.
We study deformations of Lie groupoids by means of the cohomology which controls them. This cohomology turns out to provide an intrinsic model for the cohomology of a Lie groupoid with values in its adjoint representation. We prove several fundamental properties of the deformation cohomology including Morita invariance…
The paper proves a Serre-Swan Theorem for coisotropic algebras.
problem Formalizing coisotropic reduction in Poisson geometry and deformation quantization.
method Proves a Serre-Swan Theorem relating projective modules to vector bundles.
result Equivalence of categories for simple distributions.
Theory of space-time currents for geometric evolutions.
problem Analysis of geometric evolutions driven by dislocations.
method Development of space-time integral currents with bounded variation, introduction of Lipschitz deformation distance.
result Agreement of Lipschitz deformation distance with integral Whitney flat metric for boundaryless currents.
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.
An unobstructedness theorem is proved for deformations of compact holomorphic Poisson manifolds and applied to a class of examples. These include certain rational surfaces and Hilbert schemes of points on Poisson surfaces. We study in particular the Hilbert schemes of the projective plane and show that a generic deform…
This is the second of three papers about the Compression Theorem. We give proofs of Gromov's theorem on directed embeddings [M Gromov, Partial differential relations, Springer--Verlag (1986); 2.4.5 C'] and of the Normal Deformation Theorem [The compression theorem I; 4.7], arxiv:math.GT/9712235.
Paper proves gluing formula for analytic torsions using Witten deformation for non-Morse functions.
problem Analyzing analytic torsions for non-Morse functions.
method Witten deformation, Mayer-Vietoris sequences, Vishik's theory of moving boundary problems.
result Novel, purely analytic proof of the gluing formula for analytic torsions.