Publication Date
Spring 4-11-2022
Abstract
For 2 ≤ p < 4, we study the Lp norms of restrictions of eigenfunctions of the Laplace-Beltrami operator on smooth compact 2-dimensional Riemannian manifolds. Burq, G\´erard, and Tzvetkov [12], and Hu [21] found eigenfunction restriction estimates for a curve with nonvanishing geodesic curvatures. We will explain how the proof of the known estimates helps us to consider the case where the given smooth compact Riemannian manifold has nonpositive sectional curvatures. For p = 4, we will also obtain a logarithmic analogous estimate, by using arguments in Xi and Zhang [37], Sogge [33], and Bourgain [10]. At the end of this dissertation, we will talk about a future work, which is a follow up study for higher dimensional analogues of the above curve cases.
Degree Name
Mathematics
Level of Degree
Doctoral
Department Name
Mathematics & Statistics
First Committee Member (Chair)
Matthew D. Blair
Second Committee Member
Maria Cristina Pereyra
Third Committee Member
Dimiter Vassilev
Fourth Committee Member
Melissa Evelyn Tacy
Language
English
Keywords
Eigenfunction Restriction Estimates
Document Type
Dissertation
Recommended Citation
Park, Chamsol. "Eigenfunction Restriction Estimates for Curves with Nonvanishing Geodesic Curvatures in Compact Riemannian Surfaces with Nonpositive Sectional Curvatures." (2022). https://digitalrepository.unm.edu/math_etds/169
