Zobrazeno 1 - 10
of 282
pro vyhledávání: '"Sogge, Christopher D."'
Autor:
Huang, Xiaoqi, Sogge, Christopher D.
We obtain improved Strichartz estimates for solutions of the Schr\"odinger equation on compact manifolds with nonpositive sectional curvatures which are related to the classical universal results of Burq, G\'erard and Tzvetkov [11]. More explicitly,
Externí odkaz:
http://arxiv.org/abs/2407.13026
Autor:
Sogge, Christopher D.
We discuss problems that relate curvature and concentration properties of eigenfunctions and quasimodes on compact boundaryless Riemannian manifolds. These include new sharp $L^q$-estimates, $q\in (2,q_c]$, $q_c=2(n+1)/(n-1)$, of log-quasimodes that
Externí odkaz:
http://arxiv.org/abs/2404.13739
Autor:
Huang, Xiaoqi, Sogge, Christopher D.
We show that the upper bounds for the $L^2$-norms of $L^1$-normalized quasimodes that we obtained in [9] are always sharp on any compact space form. This allows us to characterize compact manifolds of constant sectional curvature using the decay rate
Externí odkaz:
http://arxiv.org/abs/2404.13738
Autor:
Huang, Xiaoqi, Sogge, Christopher D.
We obtain new optimal estimates for the $L^2(M)\to L^q(M)$, $q\in (2,q_c]$, $q_c=2(n+1)/(n-1)$, operator norms of spectral projection operators associated with spectral windows $[\lambda,\lambda+\delta(\lambda)]$, with $\delta(\lambda)=O((\log\lambda
Externí odkaz:
http://arxiv.org/abs/2404.13734
We obtain improved Strichartz estimates for solutions of the Schr\"odinger equation on negatively curved compact manifolds which improve the classical universal results results of Burq, G\'erard and Tzvetkov [11] in this geometry. In the case where t
Externí odkaz:
http://arxiv.org/abs/2304.05247
We obtain new improved spectral projection estimates on manifolds of non-positive curvature, including sharp ones for relatively large spectral windows for general tori. Our results are stronger than those in an earlier work of the first and third au
Externí odkaz:
http://arxiv.org/abs/2211.17266
We show that if $Y$ is a compact Riemannian manifold with improved $L^q$ eigenfunction estimates then, at least for large enough exponents, one always obtains improved $L^q$ bounds on the product manifold $X\times Y$ if $X$ is another compact manifol
Externí odkaz:
http://arxiv.org/abs/2205.04489