UMD Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/3

New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.

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Author: search.filters.author.Frazier, Jeffrey RussellSubject: search.filters.subject.Curvature

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    Length Spectral Rigidity of Non-Positively Curved Surfaces
    (2011) Frazier, Jeffrey Russell; Goldman, William M.; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    Length spectral rigidity is the question of under what circumstances the geometry of a surface can be determined, up to isotopy, by knowing only the lengths of its closed geodesics. It is known that this can be done for negatively curved Riemannian surfaces, as well as for negatively curved cone surfaces. Steps are taken toward showing that this holds also for flat cone surfaces, and it is shown that the lengths of closed geodesics are also enough to determine which of these three categories a geometric surface falls into. Techniques of Gromov, Bonahon, and Otal are explained and adapted, such as topological conjugacy, geodesic currents, Liouville measures, and the average angle between two geometric surfaces.