Analysis of weighted p-harmonic forms and applications

DOI10.1142/S0129167X19500587zbMath1429.53059OpenAlexW2970400569MaRDI QIDQ5243548

Nguyen Thac Dung, Chiung-Jue Anna Sung

Publication date: 19 November 2019

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0129167x19500587

zbMATH Keywords

Sobolev inequalitysmooth metric measure spacesweighted Poincaré inequalityWeitzenböck curvature operator\(p\)-harmonic forms

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (8)

Gradient estimates for weighted \(p\)-Laplacian equations on Riemannian manifolds with a Sobolev inequality and integral Ricci bounds ⋮ Vanishing theorems for \(p\)-harmonic forms on Riemannian manifolds ⋮ p-harmonic 1-forms on totally real submanifolds in complex space forms ⋮ A note on \(p\)-harmonic \(\ell\)-forms on complete non-compact manifolds ⋮ Unnamed Item ⋮ The first nonzero eigenvalue of the p-Laplacian on differential forms ⋮ Liouville theorems for nonlinear elliptic equations on Riemannian manifolds ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Liouville type theorems for the \(p\)-harmonic functions on certain manifolds
• Smooth metric measure spaces with non-negative curvature
• Sharp gradient estimate and spectral rigidity for \(p\)-Laplacian
• Global comparison principles for the \(p\)-Laplace operator on Riemannian manifolds
• The \(p\)-hyperbolicity of infinity volume ends and applications
• On removable singularities of p-harmonic maps
• \(L^ p\) and mean value properties of subharmonic functions on Riemannian manifolds
• Uniformly elliptic operators on Riemannian manifolds
• Ends of metric measure spaces and Sobolev inequalities
• On the structure of submanifolds in Euclidean space with flat normal bundle
• Weighted Sobolev inequalities and Ricci flat manifolds
• Regularity for a more general class of quasilinear equations
• The differential form spectrum of manifolds of positive curvature
• Eigenvalue comparison theorems and its geometric applications
• A Liouville type theorem for \(p\)-harmonic maps
• \(L^2\)-cohomology and Sobolev inequalities
• Harmonic sections of polynomial growth
• Refined Kato inequalities and conformal weights in Riemannian geometry
• A Hodge theory for some non-compact manifolds.
• Complete manifolds with positive spectrum
• Complete manifolds with positive spectrum. II.
• Regularity results for differential forms solving degenerate elliptic systems
• First eigenvalue for the \(p\)-Laplace operator
• A sharp \(L^q\)-Liouville theorem for \(p\)-harmonic functions
• An exact sequence in \(L^2\)-cohomology
• Volume growth, Green's functions, and parabolicity of ends
• Topology of steady and expanding gradient Ricci solitons via f-harmonic maps
• \(p\)-harmonic functions and connectedness at infinity of complete submanifolds in a Riemannian manifold
• Constancy of \(p\)-harmonic maps of finite \(q\)-energy into non-positively curved manifolds
• Spectrum of the Laplacian on quaternionic Kähler manifolds
• Heat kernel on smooth metric measure spaces with nonnegative curvature
• A Note on p-Harmonic 1-Forms on Complete Manifolds
• HARMONIC MAPS FROM SMOOTH METRIC MEASURE SPACES
• Results on a weighted Poincaré inequality of complete manifolds
• Connectedness at infinity of complete Kähler manifolds
• On the Sobolev constant and the $p$-spectrum of a compact riemannian manifold
• Regularity of differential forms minimizing degenerate elliptic functionals.
• Sobolev and isoperimetric inequalities for riemannian submanifolds
• The heat kernel weighted Hodge Laplacian on noncompact manifolds
• Harmonic maps with finite total energy
• On weighted 𝐿² cohomology
• Sobolev and mean‐value inequalities on generalized submanifolds of Rⁿ

This page was built for publication: Analysis of weighted p-harmonic forms and applications