Title :

Lp norms, nodal sets, and quantum ergodicity

Author(s) :

Hezari, Hamid [Auteur]
Department of Mathematics [Irvine]
Rivière, Gabriel [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

English keyword(s) :

Semiclassical analysis
Eigenfunctions of the Laplacian
Negatively curved manifolds

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Théorie spectrale [math.SP]
Mathématiques [math]/Systèmes dynamiques [math.DS]

English abstract : [en]

For small range of p > 2, we improve the L p bounds of eigenfunctions of the Laplacian on negatively curved manifolds. Our improvement is by a power of logarithm for a full density sequence of eigenfunctions. We also derive ...
Show more >For small range of p > 2, we improve the L p bounds of eigenfunctions of the Laplacian on negatively curved manifolds. Our improvement is by a power of logarithm for a full density sequence of eigenfunctions. We also derive improve-ments on the size of the nodal sets. Our proof is based on a quantum ergodicity property of independent interest, which holds for families of symbols supported in balls whose radius shrinks at a logarithmic rate.Show less >

Language :

Anglais

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Comment :

27 pages

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL