Stability theorem for concordance embeddings with applications.
problem Stability of concordance embeddings.
method Proving a stability theorem.
result Various applications to diffeomorphisms and homeomorphisms.
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48 results for “embedding theorem”
Embeds pre-multisymplectic manifolds into coisotropic ones.
problem Embedding pre-multisymplectic manifolds.
method Proves a coisotropic embedding theorem.
result Validates embedding of pre-multisymplectic manifolds.
New proof shows no Hölder embeddings into Heisenberg group.
problem Non-existence of Hölder embeddings into Heisenberg group.
method Developed a new elementary proof method.
result Generalization of Gromov's theorem proven.
We consider a compact connected CR manifold with a transversal CR locally free -action endowed with a rigid positive CR line bundle. We prove that a certain weighted Fourier-Szegő kernel of the CR sections in the high tensor powers admits a full asymptotic expansion and we establish -equivariant K…
Alternative proof of coisotropic embedding theorem for pre-symplectic manifolds.
problem Proving the coisotropic embedding theorem for pre-symplectic manifolds.
method Recast geometric choice of connection as algebraic embedding into cotangent bundle, identify symplectic thickening as submanifold of Hamiltonian momenta conjugate to kernel directions.
result Alternative proof of the coisotropic embedding theorem.
Survey simplifies embedding theorems for manifolds.
problem Embedding manifolds into Euclidean space.
method Combining complement and neighborhood ideas to reduce embeddability to algebraic problems.
result Clarified exposition of Browder-Levine theorem on realization of normal systems.
The abstract discusses embedding theorems for pseudo-Kähler manifolds.
problem Embedding theorems for pseudo-Kähler manifolds.
method Using quantizable pseudo-Kähler manifolds and Hermitian line bundles, the asymptotic expansion of Bergman kernels is analyzed.
result The asymptotic expansion of Bergman kernels implies analogues of Kodaira embedding theorem and Tian's almost-isometry theorem.
Nash's theorem proved with Günther's trick
problem Proving Nash's smooth embedding theorem
method Using Günther's trick
result Nash's theorem proved
We generalise theorems of Khodorovskiy and Park-Park-Shin, and give new topological proofs of those theorems, using embedded surfaces in the 4-ball and branched double covers. These theorems exhibit smooth codimension-zero embeddings of certain rational homology balls bounded by lens spaces.
Extends symplectic reduction and theorem to Lie algebroids.
problem Symplectic reduction and theorem for Lie algebroids.
method Extends Marsden-Weinstein reduction and Darboux-Moser-Weinstein theorems.
result Obtained coisotropic embedding theorem for symplectic Lie algebroids.
We give several generalizations of the Kodaira vanishing and embedding theorems for Kähler manifolds to the case where the relevent line bundle has a small region of negative curvature. To prove the vanishing theorems we adapt techniques of Elworthy-Rosenberg for vanishing theorems in Riemannian geometry. For the embed…
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.
Five-point Toponogov theoremmath.DG
Condition for embedding metric spaces into curved manifolds.
problem Embedding conditions for metric spaces in curved manifolds.
method If-and-only-if condition on five-point metric spaces.
result Five-point metric spaces admit embeddings into nonnegatively curved Riemannian manifolds.
An complete exposition of Matthias Gunther's elementary proof of Nash's isometric embedding theorem.
The paper proves isometric embeddings for smooth manifolds.
problem Embedding smooth manifolds isometrically into Euclidean spaces.
method Nash-Kuiper's convex integration construction and gluing technique.
result Infinitely many global isometric embeddings into 2n-dimensional Euclidean space.
3D Schoenflies theorem for simply-connected 2-complexes.
problem Embedding simply-connected 2-complexes in 3-space uniquely.
method Proving a 3-dimensional Schoenflies theorem for 3-connected link graphs.
result Essentially unique locally flat embedding into 3-sphere.
The Bonnet theorem is proven for statistical manifolds.
problem Locally embeddable statistical manifolds in flat spaces.
method Using statistical embedding and the Gauss--Codazzi--Ricci equations.
result Statistical manifolds with specific tensor properties are locally embeddable to flat statistical manifolds.
Theorem proves congruence for compact submanifolds in a sphere.
problem Understanding submanifolds in a sphere with specific embedding properties.
method Used a Reilly type formula for space forms.
result Proved a congruence theorem for compact embedded hypersurfaces.
In this paper, by using analytical methods we obtain a generalization of the famous Kodaira embedding theorem.
Explains Hodge theory and Kodaira embedding theorem for complex manifolds.
problem Understanding complex manifold properties and their geometric implications.
method Expository review of harmonic forms, Hodge theory, and Kodaira embedding theorem.
result Establishes connections between de Rham cohomology, Dolbeault cohomology, and projective varieties.
An Embedding Theorem for Tractor Bundles, and an Application in Conformal Pseudo-Riemannian Geometrymath.DG
Embedding theorem for tractor bundles applied to conformal geometry.
problem Embedding theorem for tractor bundles in Cartan geometries.
method Extension of Gromov-Zimmer embedding theorem to tractor bundles.
result Rigidity result for conformal actions of special pseudo-unitary groups.
An locally conformally Kahler (LCK) manifold with potential is a complex manifold with a cover which admits an automorphic Kahler potential. An LCK manifold with potential can be embedded to a Hopf manifold, if its dimension is at least 3. We give a functional-analytic proof of this result based on Riesz-Schauder theor…
Paper proves embedding theorem for conformally compact manifolds.
problem Embedding conformally compact manifolds into hyperbolic spaces.
method Proves analogous Nash Embedding Theorem for conformally compact manifolds.
result Conformally compact manifolds can be isometrically embedded into hyperbolic spaces.
The study characterizes and verifies equivariant embeddings of symmetric Kählerian manifolds.
problem Characterizing and verifying equivariant embeddings of symmetric Kählerian manifolds.
method Investigation motivated by Cartan and Wallach's theorem on symmetric spaces, focusing on and parallel plurimean curvature.
result If an equivariant embedding has parallel plurimean curvature, it is the extrinsically symmetric one.
Notes on embedding criteria for smooth manifolds.
problem Conditions for embedding smooth manifolds into Euclidean space.
method Linking recent results to classical criteria and K-theory.
result Recent results connect to classical embedding criteria.
We present the details of our embedding proof of the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary.
Symplectic embedding extended to stratified spaces.
problem Symplectic embedding theorem for stratified spaces.
method Defined symplectic structure on stratified spaces, demonstrated embedding in complex projective space.
result Symplectic embedding theorem extended to stratified spaces.
Proves isometric embeddings in Euclidean spaces for RCD spaces.
problem Isometric immersions of RCD spaces in Euclidean spaces.
method Analyzes regular isometric immersions and eigenmaps of compact non-collapsed RCD spaces.
result Eigenmaps of compact non-collapsed RCD spaces are locally bi-Lipschitz embeddings to spheres.
In this paper, we survey some recent results about the asymptotic expansion of Bergman kernel and we give a Bergman kernel proof of Kodaira embedding theorem.
Survey on embedding 3-manifolds in definite 4-manifolds, focusing on Donaldson's theorem.
problem Understanding embeddings of 3-manifolds in definite 4-manifolds.
method Utilizes Donaldson's diagonalization theorem and combinatorics of integral lattices.
result New result on embedding amphichiral lens spaces in negative-definite manifolds.
The paper explains the topological origin of the distinction between incidence theorems over division rings and fields.
problem Understanding the distinction between incidence theorems over division rings and fields.
method Extending the surface-graph approach to noncommutative settings, the paper analyzes the topological properties of graphs embedded on surfaces of different genera.
result Theorems associated with graphs on the sphere hold over any division ring, while those on surfaces of positive genus typically hold only if the ground ring is a field.
In this paper we prove two theorems. The first one is a structure result that describes the extrinsic geometry of an embedded surface with constant mean curvature (possibly zero) in a homogeneously regular Riemannian three-manifold, in any small neighborhood of a point of large almost-maximal curvature. We next apply t…
We compare critical exponent for quasi-Fuchsian groups acting on the hyperbolic 3-space, , and on invariant disks embedded in . We give a rigidity theorem for all embedded surfaces when the action is Fuchsian and a rigidity theorem for negatively curved surfaces when the action is quasi-Fuch…
We prove that an embedded cobordism between manifolds with boundary can be split into a sequence of right product and left product cobordisms, if the codimension of the embedding is at least two. This is a topological counterpart of the algebraic splitting theorem for embedded cobordisms of the first author, A. Nemethi…
Characterizes simplicial complexes embedding into spheres with few vertices.
problem Characterizing simplicial complexes that embed into spheres with few vertices.
method Simple characterization using non-face families and analogy with Fáry's theorem.
result Recovery of van Kampen--Flores theorem and Erd\H os--Ko--Rado theorem.
The study proves a tube theorem for complex hyperbolic manifolds.
problem Understanding the geometry of complex hyperbolic manifolds.
method Tubular neighborhood theorem and geometric combination theorem.
result Explicit estimates and bounds for tube widths in complex hyperbolic manifolds.
4D theorem for disks, generalizing previous work.
problem Properly embedded disks in 4-manifolds.
method Generalization of Gabai and Kosanovic-Teichner's work, new geometric interpretation of Dax invariant.
result Homotopic disks are smoothly isotopic under certain conditions.
New examples of embeddings defy Anosov representation limits.
problem Examples of robust quasi-isometric embeddings not approximated by Anosov representations.
method Exhibited non-locally rigid, Zariski dense embeddings in .
result Higher rank Anosov representation theorems fail for .
Paper proves impossibility of three desirable properties in node embedding.
problem Understanding limitations of node embedding methods.
method Axiomatic approach to node embedding, proving impossibility of three properties.
result No node embedding method can satisfy all three desirable properties simultaneously.
Proves surface embedding theorem for 4-manifolds with good fundamental group.
problem Surface embedding in 4-manifolds with good fundamental group.
method Introduces dual spheres and Kervaire-Milnor invariant for computation.
result Combinatorial formula for Kervaire-Milnor invariant.
We examine doing probabilistic descent over manifolds implicitly defined by a set of polynomials with rational coefficients. The system of polynomials is assumed to be triangularized. An application of Whitney's embedding theorem allows us to work in a reduced dimensional embedding space. A numerical continuation metho…
Paper studies embedding conditions for homogeneous quandles.
problem Embedding problem of homogeneous quandles.
method Necessary and sufficient condition for quandle homomorphisms to be embeddings.
result Generalization of embedding theorem for generalized Alexander quandles.
Modified proof constructs dual spheres for 4-manifolds.
problem Prove dual spheres for 4-manifolds.
method Modified proof of disc embedding theorem, geometric construction.
result Constructs geometrically dual spheres.
New proof shows no flat embedding for Petersen family graphs.
problem Proving Petersen family graphs have no flat embeddings.
method Applying Böhme's Lemma and the Jordan-Brouwer Separation Theorem.
result Every Petersen family graph has no flat embedding.
In this paper we prove a theorem concerning lamination limits of sequences of compact disks embedded in with constant mean curvature , when the boundaries of these disks tend to infinity. This theorem generalizes to the non-zero constant mean curvature case Theorem 0.1 by Colding and Minicozzi…
We obtain an embedding theorem for compact strongly pseudoconvex CR manifolds which are bounadries of some complete Hermitian manifolds. We use this to compactify some negatively curved Kaehler manifolds with compact strongly pseudoconvex boundary. An embedding theorem for Sasakian manifolds is also derived.
Let M be a compact Sasakian manifold. We show that M admits a CR-embedding into a Sasakian manifold diffeomorphic to a sphere, and this embedding is compatible with the respective Reeb fields. We argue that a stronger embedding theorem cannot be obtained. We use an extension theorem for Kaehler geometry: given a compac…
New theorem shows embedding restrictions for manifold skeletons.
problem Embedding restrictions for triangulated manifolds.
method Proves van Kampen-Flores theorem for manifolds with specific Stiefel-Whitney classes.
result Triangulated manifolds with non-trivial Stiefel-Whitney classes cannot embed into .