常曲率空间上球面均值变换的值域描述
微分几何
2011-09-28 v2 偏微分方程分析
度量几何
摘要
我们描述了一种受限球面均值变换的值域，该变换将支撑在双曲空间中闭球内的函数映射为其在球心位于球边界上的测地球面上的均值。该描述类似于 Mark Agranovsky、David Finch 和 Peter Kuchment [Inverse Problems and Imaging, 3(3):373--382, 2009] 以及 Mark Agranovsky 和 Linh V. Nguyen [J. Anal. Math., 112:351--367, 2010] 在欧氏空间上获得的同一变换的描述。我们还推导了二维球面空间上相应变换的类似刻画。
引用
@article{arxiv.1107.1746,
title = {Range description for a spherical mean transform on spaces of constant curvatures},
author = {Linh V. Nguyen},
journal= {arXiv preprint arXiv:1107.1746},
year = {2011}
}
备注
In the second version, we corrected some minor mistakes in the proof of Theorem 2.1. We added the result for the two dimensional spherical space. We also changed the tittle to reflect the new content of the paper