Let be a Kahler manifold. An integrable function on M is called -plurisubharmonic if it is subharmonic on all q-dimensional complex subvarieties. We prove that a smooth -plurisubharmonic function is q-convex. A continuous -plurisubharmonic function admits a local approximation by smooth, -pl…
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10 results for “q-convexity”
Study on Hodge decompositions for Lie algebroids on manifolds with boundary.
problem When does the Chevalley-Eilenberg differential admit a Hodge decomposition?
method Introduce concepts like Cauchy-Riemann structures, elliptic and non-elliptic boundary points, q-convexity, and use them to prove Hodge decompositions.
result Hodge decompositions for q-convex elliptic Lie algebroids on manifolds with boundary.
The study proves conditions for convex hypersurfaces in Riemannian manifolds to be rational homology spheres.
problem Conditions for convex hypersurfaces to be rational homology spheres in Riemannian manifolds.
method The study proves conditions for convex hypersurfaces in Riemannian manifolds to be rational homology spheres using vanishing and estimation theorems for Betti numbers.
result Conditions for convex hypersurfaces to be rational homology spheres in Riemannian manifolds.
Unified proofs of weak holomorphic Morse inequalities using Bergman kernel functions.
problem Weak holomorphic Morse inequalities on various types of manifolds.
method Asymptotic Bergman kernel functions and Bochner-Kodaira-Nakano formulas.
result Unified proofs of weak holomorphic Morse inequalities.
The paper proves optimal estimates and inequalities for spectral functions on certain manifolds.
problem Optimal estimates and inequalities for spectral functions on weakly 1-complete manifolds.
method Establishes optimal fundamental estimates and weak Morse inequalities for lower energy forms.
result Optimal fundamental estimates and weak Morse inequalities are proven for lower energy forms on weakly 1-complete manifolds.
Estimates cohomology dimensions for Nakano q-semipositive line bundles.
problem Estimating cohomology dimensions for Nakano q-semipositive line bundles.
method Asymptotic estimates for high tensor powers of semipositive line bundles over q-convex manifolds and various complex manifolds.
result Optimal order estimates for cohomology dimensions.
The aim of this article is to understand the geometry of limit sets in pseudo-Riemannian hyperbolic geometry. We focus on a class of subgroups of introduced by Danciger, Guéritaud and Kassel, called -convex cocompact. We define a pseudo-Riemannian analogue of critical exponent and…
The paper estimates the dimension of cohomology for semipositive line bundles on various manifolds.
problem Estimating the dimension of cohomology for semipositive line bundles over different types of manifolds.
method Asymptotic estimates for harmonic -forms with high tensor powers of semipositive line bundles.
result Asymptotic estimates for the dimension of cohomology of semipositive line bundles on various manifolds.
New Teichmüller spaces found for higher-dimensional groups.
problem Finding new Teichmüller spaces for higher-dimensional groups.
method Proving representations of groups in pseudo-Riemannian hyperbolic spaces are convex cocompact.
result Set of representations forms connected components of Hom spaces.
The paper proves extension theorems for complex manifolds with Levi -concave domains.
problem Holomorphic extension theorems for complex manifolds with Levi -concave domains.
method The proof relies on holomorphic Morse inequalities, the Kohn-Rossi extension theorem, and a general Nakano-Griffiths inequality.
result Holomorphic extension theorems for -forms on Levi -concave domains.