Generic injectivity and stability of inverse problems for connections
Generic injectivity and stability of inverse problems for connections
复制标题
连接反问题的一般内射性和稳定性
DOI：
10.1080/03605302.2017.1295061
复制
发表时间：
2016
影响因子：
1.9
通讯作者：
Hanming Zhou
中科院分区：
文献类型：
--
作者：
Hanming Zhou
本文考虑了在任意维的紧致黎曼流形上，由相应的平行输运沿着测地线确定一个联络和一个Higgs场的非线性问题。通过伪线性化的论证，该问题可以归结为某个衰减测地线变换的积分几何问题。我们显示注入性（自然障碍）和稳定性估计的线性和非线性问题的通用简单的度量和通用连接和希格斯场，包括真正的分析。我们考虑了单流形上的问题，使主要思想的阐述简洁明了，本文的许多结果在某些弱于单性的假设下仍然成立。
ABSTRACT We consider the nonlinear problem of determining a connection and a Higgs field from the corresponding parallel transport along geodesics on a compact Riemannian manifold with boundary, in any dimension. The problem can be reduced to an integral geometry question of some attenuated geodesic ray transform through a pseudolinearization argument. We show injectivity (up to natural obstructions) and stability estimates for both the linear and nonlinear problems for generic simple metrics and generic connections and Higgs fields, including the real-analytic ones. We consider the problems on simple manifolds to make the exposition of the main ideas clear and concise, many results of this paper still hold under some assumptions weaker than simplicity.