Tensor tomography on surfaces

• 成果类型: Article
• 署名作者: Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther
• 署名单位: University of Cambridge; University of Jyvaskyla; University of Washington; University of Washington Seattle; University of California System; University of California Irvine
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-012-0432-1
• 发表日期: 2013
• 页码: 229-247
• 关键词: integral geometry problem; attenuated ray transform; connections; RIGIDITY; FIELDS

摘要

We show that on simple surfaces the geodesic ray transform acting on solenoidal symmetric tensor fields of arbitrary order is injective. This solves a long standing inverse problem in the two-dimensional case.