<mods:mods xmlns:mods="http://www.loc.gov/mods/v3" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:METS="http://www.loc.gov/METS/" ID="etd444" xsi:schemaLocation="http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd">
          <mods:titleInfo>
            <mods:title>The Geometry of the Space of 2D Shapes and theWeil-Petersson Metric</mods:title>
          </mods:titleInfo>
          <mods:name type="personal">
            <mods:namePart>Kushnarev, Sergey </mods:namePart>
            <mods:role>
              <mods:roleTerm type="text">creator</mods:roleTerm>
            </mods:role>
          </mods:name>
          <mods:originInfo>
            <mods:copyrightDate>2010</mods:copyrightDate>
          </mods:originInfo>
          <mods:physicalDescription>
            <mods:extent>xviii, 140 p.</mods:extent>
            <mods:digitalOrigin>born digital</mods:digitalOrigin>
          </mods:physicalDescription>
          <mods:note>Thesis (Ph.D. -- Brown University (2010)</mods:note>
          <mods:name type="personal">
            <mods:namePart>Mumford, David</mods:namePart>
            <mods:role>
              <mods:roleTerm type="text">Director</mods:roleTerm>
            </mods:role>
          </mods:name>
          <mods:name type="personal">
            <mods:namePart>Michor, Peter</mods:namePart>
            <mods:role>
              <mods:roleTerm type="text">Reader</mods:roleTerm>
            </mods:role>
          </mods:name>
          <mods:name type="personal">
            <mods:namePart>Geman, Stuart</mods:namePart>
            <mods:role>
              <mods:roleTerm type="text">Reader</mods:roleTerm>
            </mods:role>
          </mods:name>
          <mods:name type="corporate">
            <mods:namePart>Brown University. Applied Mathematics</mods:namePart>
            <mods:role>
              <mods:roleTerm type="text">sponsor</mods:roleTerm>
            </mods:role>
          </mods:name>
          <mods:genre authority="aat">theses</mods:genre>
          <mods:abstract>This thesis investigates three related topics on the geometry of the space of planarshapes.In the first part, we setup the EPDiff (Euler-Poincare equation on the group ofdiffeomorphisms) and investigate its singular solutions, Teichons, analogues of solitons.A symplectic integration scheme has been implemented to solve a Hamiltonianproblem that arises in this part.In the second part, the formula for the sectional curvature of the Weil-Peterssonmetric has been derived. It has been shown that the formula coincides with Arnold'sformula in the case of the metric without a null space.The third part concerns numerical implementation of optimization problem offinding geodesics by minimizing the Weil-Petersson energy. The comparison of methodsis shown alongside with the examples of geodesics.</mods:abstract>
          <mods:subject>
            <mods:topic>shape space</mods:topic>
          </mods:subject>
          <mods:subject>
            <mods:topic>Weil-Petersson metric</mods:topic>
          </mods:subject>
          <mods:subject>
            <mods:topic>EPDiff</mods:topic>
          </mods:subject>
          <mods:subject>
            <mods:topic>Teichons</mods:topic>
          </mods:subject>
          <mods:subject>
            <mods:topic>universal Teichmuller space</mods:topic>
          </mods:subject>
          <mods:subject>
            <mods:topic>diffeomorphism group</mods:topic>
          </mods:subject>
          <mods:recordInfo>
            <mods:recordContentSource authority="marcorg">RPB</mods:recordContentSource>
            <mods:recordCreationDate encoding="iso8601">20111003</mods:recordCreationDate>
          </mods:recordInfo>
        <mods:language><mods:languageTerm type="code" authority="iso639-2b">eng</mods:languageTerm><mods:languageTerm type="text">English</mods:languageTerm></mods:language><mods:identifier type="doi">10.7301/Z04T6GK8</mods:identifier><mods:accessCondition type="rights statement" xlink:href="http://rightsstatements.org/vocab/InC/1.0/">In Copyright</mods:accessCondition><mods:accessCondition type="restriction on access">Collection is open for research.</mods:accessCondition><mods:typeOfResource authority="primo">dissertations</mods:typeOfResource></mods:mods>