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Scattering and lens rigidity.
- Format:
- Book
- Thesis/Dissertation
- Author/Creator:
- Wen, Haomin, author.
- Language:
- English
- Subjects (All):
- Mathematics.
- Mathematics--Penn dissertations.
- Penn dissertations--Mathematics.
- Local Subjects:
- Mathematics.
- Mathematics--Penn dissertations.
- Penn dissertations--Mathematics.
- Genre:
- Academic theses.
- Physical Description:
- 1 online resource (53 pages)
- Contained In:
- Dissertation Abstracts International 75-10B(E).
- Place of Publication:
- [Philadelphia, Pennsylvania] : University of Pennsylvania ; Ann Arbor, MI : ProQuest, 2014.
- System Details:
- Mode of access: World Wide Web.
- text file
- Summary:
- Scattering rigidity of a Riemannian manifold allows one to tell the metric of a manifold with boundary by looking at the directions of geodesics at the boundary. Lens rigidity allows one to tell the metric of a manifold with boundary from the same information plus the length of geodesics. There are a variety of results about lens rigidity but very little is known for scattering rigidity. We will discuss the subtle difference between these two types of rigidities and prove that they are equivalent for two-dimensional simple manifolds with boundaries. In particular, this implies that two-dimensional simple manifolds (such as the at disk) are scattering rigid since they are lens/boundary rigid (Pestov--Uhlmann, 2005).
- Notes:
- Source: Dissertation Abstracts International, Volume: 75-10(E), Section: B.
- Adviser: Christopher Croke.
- Department: Mathematics.
- Thesis Ph.D. University of Pennsylvania 2014.
- Local Notes:
- School code: 0175.
- ISBN:
- 9781303969386
- Access Restriction:
- Restricted for use by site license.
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