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SUMMARY:Tracey Balehowsky (University of Helsinki)
DTSTART:20210916T160000Z
DTEND:20210916T170000Z
DTSTAMP:20260423T035752Z
UID:Inverse/57
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Inverse/57/"
 >Determining a Riemannian metric from least-area data</a>\nby Tracey Baleh
 owsky (University of Helsinki) as part of International Zoom Inverse Probl
 ems Seminar\, UC Irvine\n\n\nAbstract\nIn this talk\, we address the follo
 wing question: Given any simple closed curve $\\gamma$ on the boundary of 
 a Riemannian 3-manifold $(M\,g)$\, suppose the area of the least-area surf
 aces bounded by $\\gamma$ are known. From this data may we uniquely recove
 r $g$? \n\nIn several settings\, we show the the answer is yes. In fact\, 
 we prove both global and local uniqueness results given least-area data fo
 r a much smaller class of curves on the boundary. We demonstrate uniquenes
 s for $g$ by reformulating parts of the problem as a 2-dimensional inverse
  problem on an area-minimizing surface. In particular\, we relate our leas
 t-area information to knowledge of the Dirichlet-to-Neumann map for the st
 ability operator on a minimal surface. \n\nBroadly speaking\, the question
  we address is a dimension 2 version of the classical boundary rigidity pr
 oblem for simply connected\, Riemannian 3-manifolds with boundary. We will
  briefly review this problem of boundary rigidity as it relates to aspects
  of our question of recovering $g$ from knowledge of areas. \n\nThis is jo
 int work with S. Alexakis and A. Nachman.\n
LOCATION:https://researchseminars.org/talk/Inverse/57/
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