Abstract: Sogge’s Lp estimates bound the Lp norms of normalized eigenfunctions on smooth and compact manifolds. They are also sharp on the sphere, with maximizers as Gaussian beams for small p and zonal harmonics for large p. In this talk, we investigate the density of these maximizers in the orthonormal eigenfunction basis, and construct a positive density subsequence of orthonormal spherical harmonics which achieves the maximal Lp norm growth for all small p. This gives an example of a Riemannian surface supporting such subsequence of eigenfunctions. Furthermore, we provide an explicit lower bound on the density in this example.

 

祝好!