By a theorem of Greene and Wu, a noncompact connected Riemannian manifold admits a smooth strictly subharmonic exhaustion function. Demailly provided an elementary proof of this fact. A further simplification of Demailly's proof and some (mostly known) applications are described. Applications include the fact that the …
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48 results for “subharmonic exhaustions”
This work explores duality between nonlinear potential theory and geometry.
problem Investigating properties of nonlinear equations on manifolds.
method Analyzing parabolicity and maximum principles at infinity for non-linear equations.
result Shows a unifying duality between properties and existence of Khas'minskii potentials.
Study subharmonic functions in strongly symmetric Riemannian manifolds, proving polynomial growth.
problem Properties of subharmonic functions in Riemannian manifolds with a pole.
method Introduced polynomial growth of subharmonic functions and proved their properties.
result Proved polynomial growth of degree 1 for non-negative subharmonic functions.
Introduces Reshetnyak's subharmonic distances theory.
problem No specific problem stated; focuses on theory introduction.
method No specific method mentioned; focuses on theory introduction.
result Provides an overview of Reshetnyak's subharmonic distances theory.
Study of complex Hessian equations using subharmonic functions and geodesics.
problem Understanding geodesics within complex Hessian equations.
method Perron envelope construction, comparison principle, rooftop equality, Kiselman minimum principle.
result Established criterion for geodesic connectivity among -subharmonic functions.
Geodesics found in a metric space of m-subharmonic functions.
problem Metric structure on energy class of m-subharmonic functions.
method Inspired by Kähler geometry, introduced a metric structure and studied metric convergence.
result Geodesics constructed in a subspace of the complete metric space.
The paper connects convex functions to p-subharmonic functions and proves their equivalence.
problem Understanding the relationship between convex functions and p-subharmonic functions.
method Average principle, variational methods, and PDE techniques.
result Convex functions on R^n are p-subharmonic for every p > 1.
Study singularities of -subharmonic functions along submanifolds.
problem Understanding the singularities of -subharmonic functions along complex submanifolds.
method Analyzing the growth rate and singularities of -subharmonic functions along submanifolds of a compact Kähler manifold.
result For , -subharmonic functions have at worst log poles along submanifolds with constant strength.
Study sharp decay of capacity for subharmonic functions on compact Hermitian manifolds.
problem Sharp decay of capacity of sublevel sets of -subharmonic functions.
method Generalizes previous results on Kähler manifolds and obtains full characterizations of polar sets.
result Full characterizations of polar sets and extremal functions.
New subharmonicity concept proves conjecture on Riemannian manifolds.
problem Proving positivity of solutions to a specific PDE on Riemannian manifolds.
method Introducing local -shift defectivity and studying it on locally smoothing spaces.
result Proof of Braverman, Milatovic, Shubin conjecture on positivity of solutions.
The study links Ricci curvature and convexity in complex tori.
problem Characterizing Ricci curvature signs in toric manifolds.
method Characterization through convexity of volume functional.
result Relationships between Ricci curvature, volume, submanifolds, and pluri-subharmonic functions.
Solves Dirichlet problem for generalized Hitchin's equation on cyclic Higgs bundles.
problem Existence and uniqueness of solutions to the Dirichlet problem.
method Formulated using subharmonic functions; generalizes Hitchin's equation for diagonal harmonic metrics on cyclic Higgs bundles.
result Existence and uniqueness of solutions to the Dirichlet problem.
Estimates for polynomial operators using determinant majorization and subharmonics.
problem Bounding solutions of polynomial operators on Euclidean domains.
method Combines Alexandrov estimate and determinant majorization, using subharmonics and semiconvex approximation.
result Includes classical Alexandrov-Bakelman-Pucci estimate for linear operators.
Subharmonicity of Dirichlet energy proven for Kähler manifolds.
problem Subharmonicity of Dirichlet energy in Kähler families.
method Polarized family of compact Kähler manifolds, pluriharmonic maps, nonpositive complexified sectional curvature.
result Dirichlet energy is subharmonic in the parameter space.
The paper proves three circles theorems and Liouville type theorems for subharmonic and holomorphic functions.
problem Establishing theorems for subharmonic and holomorphic functions on specific geometric structures.
method Using subharmonic and holomorphic functions on Riemannian manifolds and gradient shrinking Ricci solitons.
result Proves Liouville type theorems as applications of the established theorems.
Study proves radial symmetry in convex cones using subharmonic functions.
problem Proving radial symmetry in convex cones with boundary conditions.
method Using maximum principle and integral identities for subharmonic functions.
result Proves radial symmetry and Serrin-type results for partially overdetermined problems.
The paper extends decay estimates to graphs with positive spectrum.
problem Proving decay estimates for nonnegative functions on graphs.
method Sharp decay estimates for nonnegative generalized subharmonic functions.
result Extends Li and Wang's result to graphs with positive Laplacian spectrum.
A characterization of the degenerate complex Hessian equations for functions with bounded -energymath.CV
Characterizes complex Hessian equations for bounded energy functions.
problem Understanding degenerate complex Hessian equations for bounded energy functions.
method Proving sublevel set estimates and using Sobolev inequalities.
result Characterization of degenerate complex Hessian equations for bounded -energy functions.
Richberg technique adapted for nonlinear subequations.
problem Approximating strictly subharmonic functions in -potential theory.
method Adapting Richberg technique to -potential theory.
result Local approximation to global approximation for subharmonic functions.
Theory developed for complex Hessian measures on Hermitian manifolds.
problem Defining and analyzing complex Hessian measures on Hermitian manifolds.
method Potential theory for m-subharmonic functions with respect to a Hermitian metric.
result Equivalence between polar sets and negligible sets for m-subharmonic functions.
Convex functions defined on metric spaces are pulled back to subharmonic ones by harmonic mapsmath.MG
Harmonic maps pull convex functions on metric spaces to subharmonic ones.
problem Understanding how convex functions behave under harmonic maps on metric spaces.
method Proving subharmonicity of pullbacks of convex functions by harmonic maps in metric spaces.
result The pullback of a convex function by a harmonic map is subharmonic in metric spaces.
The paper proves a formula for complex Monge-Ampère equations on manifolds.
problem Proving a mean value formula for complex Monge-Ampère equations.
method Using subharmonic Hermitian matrix valued functions and Liouville type theorems.
result Obtained a Liouville theorem for complex Monge-Ampère equations.
This paper is a sequel to \cite{Choi} in Math. Ann. In that paper we studied the subharmonicity of Kähler-Einstein metrics on strongly pseudoconvex domains of dimension greater than or equal to . In this paper, we study the variations Kähler-Einstein metrics on bounded strongly pseudoconvex domains of dimension .…
Defines relative $\dbar$-complex and studies its curvature properties.
problem Curvature properties of relative $\dbar$-complex and associated vector bundles.
method Definition and study of curvature properties of the relative $\dbar$-complex and associated vector bundles.
result Yamaguchi's theory on subharmonicity of the Green operator can be seen as a curvature property of the quotient bundle.
The paper extends the uniqueness of complete harmonic metrics to subharmonic weights and proves their existence on the unit disc.
problem Finding complete harmonic metrics on Riemann surfaces for subharmonic weights.
method Extending Li-Mochizuki's theorem to subharmonic weights and proving existence on the unit disc.
result Complete harmonic metrics exist on the unit disc for subharmonic weights.
The paper proves a numerical condition for solving complex Hessian quotient equations with Calabi symmetry.
problem Solvability of complex Hessian quotient equations with specific symmetry.
method Proving a numerical condition and proposing a conjecture on existence of -subharmonic representatives.
result Numerical condition ensures solvability of complex Hessian quotient equations.
Study generalizes Hermitian-Einstein equation for cyclic Higgs bundles, proving existence and inequality.
problem Addressing Hermitian-Einstein equation for cyclic Higgs bundles.
method Introducing generalizations using subharmonic functions and proving existence, uniqueness, and convergence of heat equations.
result Existence, uniqueness, and convergence of solutions for heat equations.
Characterizes gradient Yamabe solitons with specific conditions.
problem Understanding properties of gradient Yamabe solitons.
method Proved conditions leading to constant scalar curvature, subharmonicity, and harmonic potential.
result Gradient Yamabe solitons under certain conditions are of constant scalar curvature.
Study shows properties of noncompact hypersurfaces in hyperbolic space.
problem Characterize noncompact hypersurfaces in hyperbolic space with nonnegative Ricci curvature.
method Utilized properties of n-subharmonic functions to analyze asymptotic boundaries.
result Hypersurfaces with nonnegative Ricci curvature in hyperbolic space have at most two points in their asymptotic boundary.
Study of interactions between functions on manifolds via submersions.
problem Understanding interactions between convex, subharmonic, and pluri-subharmonic functions on manifolds.
method Application of pluri-potential theory and analysis of Kähler and G2 manifolds.
result Previous results on Lagrangian fibrations can be viewed as applications of this framework.
We derive a local Gaussian upper bound for the -heat kernel on complete smooth metric measure space with nonnegative Bakry-Émery Ricci curvature, which generalizes the classic Li-Yau estimate. As applications, we obtain a sharp -Liouville theorem for -subharmonic functions and an -u…
The paper quantifies the singular sets of F-subharmonic functions, proving their dimensionality and rectifiability.
problem Understanding the singular sets of F-subharmonic functions and their stratification.
method Defined quantitative stratification, used Minkowski estimates, and introduced new geometric subequations.
result Proved the dimensionality and rectifiability of the singular sets of F-subharmonic functions.
The paper connects harmonic mappings to Ricci flow using geometric analysis.
problem Global geometry of harmonic mappings and Ricci solutions.
method Geometric analysis, focusing on subharmonic functions.
result Results on connections between manifold geometry and subharmonic functions.
Study rigidifies non-compact manifolds with specific curvature conditions.
problem Analyzing non-compact generalized m-quasi-Einstein manifolds with constant scalar curvature and soliton function.
method Introduced a weighted function and proved its subharmonicity to derive rigidity results.
result Proves manifolds are Euclidean under specific conditions, with constant μ essential.
The paper proves manifold isometries for certain gradient Ricci solitons.
problem Characterizing isometry of gradient shrinking Ricci solitons.
method Analyzing volume growth, scalar curvature, and potential function subharmonicity.
result Gradient shrinking Ricci solitons with specific properties are isometric to spheres or other specific manifolds.
We establish dimension-independent estimates related to heat operators e^{tL} on manifolds. We first develop a very general contractivity result for Markov kernels which can be applied to diffusion semigroups. Second, we develop estimates on the norm behavior of harmonic and non-negative subharmonic functions. We apply…
The study proves non-existence theorems for Codazzi tensors on Riemannian manifolds.
problem Proving non-existence theorems for Codazzi tensors on Riemannian manifolds.
method Using theorems connecting manifold geometry and subharmonic functions.
result Several Liouville-type non-existence theorems for Codazzi tensors.
Study exhausts curve complex on nonorientable surfaces using finite rigid sets.
problem Exhausting curve complexes on nonorientable surfaces.
method Using finite rigid sets to exhaust curve complex.
result Improves exhaustion result for or .
For nonorientable surfaces, curve complexes can be exhausted by finite superrigid sets.
problem Exhausting curve complexes on nonorientable surfaces.
method Using finite superrigid sets for exhaustion.
result An exhaustion of curve complexes by finite superrigid sets for and .
The paper studies entropy of harmonic metrics on cyclic Higgs bundles.
problem Quantifying the degree of mutual misalignment of Hermitian metrics.
method Introduces entropy function and estimates its bounds for cyclic Higgs bundles.
result Entropy difference converges to a finite real number for .
We are analysing the convexity and continuity properties of the Mabuchi functional along weak geodesics. The key technical point in our paper is the global approximation of weak geodesics obtained via a well-chosen family of Monge-Ampère equations.
This paper exhausts curve complexes on non-orientable surfaces.
problem Proving exhaustion of curve complexes on non-orientable surfaces.
method Proving exhaustion via rigid expansions and graph endomorphisms.
result Any graph endomorphism of curve complexes whose restriction to a finite rigid set is injective is induced by a homeomorphism.
Develops potential theory for WZW equation in Kähler potentials space.
problem Solving the Wess--Zumino--Witten equation in Kähler potentials.
method Introduces -harmonicity on graphs to characterize the WZW equation and uses subharmonic distance.
result Shows solvability of Dirichlet problem and approximation by finite-dimensional maps.
Study on existence and properties of continuous solutions to complex Hessian equations.
problem Existence and properties of continuous solutions to complex Hessian equations.
method Established new capacity estimates and weak stability estimates for the -Hessian measure.
result Existence of continuous solutions to the complex Hessian equation under certain conditions.
We study the problem of removable singularities for degenerate elliptic equations. Let F be a fully nonlinear second-order partial differential subequation of degenerate elliptic type on a manifold X. We study the question: Which closed subsets E in X have the property that every F-subharmonic function (subsolution) on…
Pseudo-holomorphic curves on almost complex manifolds have been much more intensely studied than their "dual" objects, the plurisubharmonic functions. These functions are defined classically by requiring that the restriction to each pseudo-holomorphic curve is subharmonic. In this paper subharmonic functions are define…
Proposes methods for selecting sparse variables in linear regression.
problem Selecting sparse variables in linear regression models.
method K-sparse exhaustive search (ES-K) and K-sparse approximate exhaustive search (AES-K) methods.
result AES-K method effectively reconstructs density of states for large problems.
We consider a complete noncompact smooth metric measure space and the associated drifting Laplacian. We find sufficient conditions on the geometry of the space so that every nonnegative -subharmonic function with bounded weighted norm is constant.