Paper proves rigidity for certain PDEs on compact manifolds.
problem Proving rigidity for -Laplace and -Laplace equations.
method Nonlinear flow and carré du champ methods.
result Rigidity means only constant solutions for certain parameters.
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5 results for “n-Laplace”
The paper extends Huber's theorem to higher dimensions using n-Laplace equations.
problem Proving finite point conformal compactification for general dimensions.
method Using n-Laplace equations and strengthened Arsove-Huber's theorem.
result Established finite point conformal compactification theorem for manifolds.
Study critical quasilinear equations on Riemannian manifolds with curvature constraints.
problem Investigate critical quasilinear elliptic equations on Riemannian manifolds with nonnegative Ricci curvature.
method Utilize a new nonlinear Kato inequality and Cheng-Yau type gradient estimates for positive solutions.
result Classify positive solutions to the critical -Laplace equation and show rigidity concerning the ambient manifold.
New geometric aspects of Moser-Trudinger inequalities on Riemannian manifolds: the non-compact casemath.AP
In the first part of the paper we investigate some geometric features of Moser-Trudinger inequalities on complete non-compact Riemannian manifolds. By exploring rearrangement arguments, isoperimetric estimates, and gluing local uniform estimates via Gromov's covering lemma, we provide a Coulhon, Saloff-Coste and Varopo…
Study -superharmonic functions and their geometric applications.
problem Asymptotic behavior of -superharmonic functions at isolated singularities.
method Using Wolff potential, -capacity estimates, and Adams-Moser-Trudinger inequality.
result Strong -capacity lower bound estimate for geometric applications.