arXiv research

Paper generalizes complex Brunn-Minkowski theory and proves new extension theorems.

The abstract presents a new theorem using Ross-Witt Nyström correspondence and Berndtsson's theorem.

Paper extends Ohsawa-Takegoshi theorem to more general domains, proving removable singularities for plurisubharmonic functions.

Using $L^2$-methods for the $\bar\partial$-equation we prove that the Ohsawa-Takegoshi extension theorem also holds for holomorphic sections of a vector bundle, over compact Kähler manifolds. We then proceed to show that the conditions that are needed are more liberal than the ones one would need if one instead reduced…

Study asymptotics of extension and orthogonal Bergman kernels for high tensor powers of positive line bundles.

New extension theorem for projective manifolds.

Paper proves integrability and entropy compactness for Kähler potentials with uniform log-log threshold.

In this paper we study the problem of extension of holomorphic sections of line bundles/vector bundles from reduced unions of strata of divisors. An extension theorem of Ohsawa--Takegoshi type is proved. As consequences we deduce several qualitative results on extension from snc divisors and generic global generation o…

A new proof of an extension theorem with bounded generators.

Study optimal holomorphic extensions on complex manifolds with transitivity property.

The paper defines positivity for singular metrics on vector bundles and proves related theorems.

Study extends complex sections on non-holomorphic objects on Kähler manifolds.

The paper characterizes positivity of holomorphic vector bundles via $L^p$-estimates and extensions.

In this paper we prove a new version of the Schoenflies extension theorem for collared domains in Euclidean n-space: for 1 < p < n, locally bi-Lipschitz homeomorphisms between collared domains with locally p-integrable, second-order weak derivatives admit homeomorphic extensions of the same regularity. Moreover, the th…

Optimal L2 extension theorem for holomorphic vector bundles with singular metrics.

Proves Skoda's Division Theorem using degeneration and positivity of direct image bundles.

Study extends isometric immersions using submanifolds.

We establish cohomological and extension dimension versions of the Hurewicz dimension-raising theorem

Paper extends theorem on covering spaces and Jordan curves.

We give a complementary generalization of the extensions of Bonnet-Myers theorem obtained by Calabi and also Cheeger-Gromov-Taylor.

Vanishing result for cohomology leads to extension theorem for pluriharmonic functions.

We show that there is no analog of Kirszbraun's extension theorem for Almgren's multiple valued functions.

We prove an extension theorem for Kahler currents with analytic singularities in a Kahler class on a complex submanifold of a compact Kahler manifold.

New Klein-Maskit theorems for Anosov subgroups.

In this article, we prove a Kahler extension theorem for real Kahler submanifolds of codimension 4 and rank at least 5. Our main theorem states that such a manifold is a holomorphic hypersurface in another real Kahler submanifold of codimension 2. This generalizes a result of Dajczer and Gromoll in 1997 which states th…

In this paper, we will give an extension of Mok's theorem on the generalized Frankel conjecture under the condition of the orthogonal bisectional curvature.

Extends Seeley's theorem for Bastiani's differential calculus in infinite dimensions.

In this paper, we obtain two extension theorems for cohomology classes and holomorphic sections defined on analytic subvarieties, which are defined as the supports of the quotient sheaves of multiplier ideal sheaves of quasi-plurisubharmonic functions with arbitrary singularities. The first result gives a positive answ…

In this paper, we first investigate the integral curvature condition to extend the mean curvature flow of submanifolds in a Riemannian manifold with codimension $d\geq1$, which generalizes the extension theorem for the mean curvature flow of hypersurfaces due to Le-Šešum \cite{LS} and the authors \cite{XYZ1,XYZ2}. Usin…

The paper extends Bonnet-Myers theorem for manifolds with nonnegative Ricci curvature.

The paper proves extension theorems for complex manifolds with Levi $q$-concave domains.

In this paper, we prove the extensions of Bonnet--Myers' type theorems obtained by Calabi and Cheeger--Gromov--Taylor via Bakry--Emery Ricci curvature, which generalize the results of \cite{FG, Lim1, Wan, Wang, WW, Wu}.

We define the geometric complex associated to a Morse-Bott-Smale vector field, cf. [Austin-Braam, 1995], and its associated spectral sequence. We prove an extension of the Bismut-Zhang theorem to Morse-Bott-Smale functions. The proof is based on the Bismut-Zhang theorem for Morse-Smale functions, see [Bismut-Zhang, 199…

This paper extends the Good Covering Theorem and Jordan Curve Theorem for proximal Alexandrov spaces.

The proof of Theorem 7.12 of "Uniqueness of smooth cohomology theories" by the authors of this note is not correct. The said theorem identifies the flat part of a differential extension of a generalized cohomology theory E with ER/Z (there called "smooth extension"). In this note, we give a correct proof. Moreover, we …

Classifies solvable symplectic Lie algebras via extensions and proves structural theorems.

We give a new variant of $L^2$-extension theorem for the jets of holomorphic sections and discuss the relation between the extension problem of singular Hermitian metrics with semipositive curvature.

The abstract discusses extensions of Jacobi groups and their orbit space properties.

The paper is devoted to generalization of well-known Michael's Selection theorem on the case of extension dimension.

In this paper we introduce a general notion of weak extension property for embeddings induced by a group actions. As an example, for the group H(M, m) of measure-preserving homeomorphisms of a noncompact manifold M, we deduce weak type extension theorems, and as an application we exhibit the local contractibility of th…

In this paper we give an extension of the Cartier-Gabriel-Kostant structure theorem to Hopf algebroids.

Estimates mean curvature flow with geometric bounds.

The paper proves a theorem about earthquake extensions of vector fields on circles.

For a complete Riemannian manifold $M$ with an (1,1)-elliptic Codazzi self-adjoint tensor field $A$ on it, we use the divergence type operator ${L_A}(u): = div(A\nabla u)$ and an extension of the Ricci tensor to extend some major comparison theorems in Riemannian geometry. In fact we extend theorems like mean curvature…

We present an extension of Dunwoody's theory of tracks and use it to prove an analogue of the annulus theorem for hyperbolic groups.

Employing Morse theory for the global control of monodromy and the method of analytic discs for local extension, we establish a version of the global Hartogs extension theorem in a singular setting: for every domain D of an (n-1)-complete normal complex space X of pure dimension n >= 2 and for every compact set K in D …

We prove an extension of a theorem of Barta then we make few geometric applications. We extend Cheng's lower eigenvalue estimates of normal geodesic balls. We generalize Cheng-Li-Yau eigenvalue estimates of minimal submanifolds of the space forms. We prove an stability theorem for minimal hypersurfaces of the Euclidean…

We formulate extensions of Wilking's Jacobi field splitting theorem to uniformly positive sectional curvature and also to positive and nonnegative intermediate Ricci curvatures.