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9 papers · 1 filter
Boundary regularity for the Ricci equation, geometric convergence, and Gel'fand's inverse boundary problem
Michael T. Anderson, Atsushi Katsuda, Yaroslav Kurylev +2
This paper explores and ties together three themes. The first is to establish regularity of a metric tensor, on a manifold with boundary, on which there are given Ricci curvature b…
Circles and Quadratic Maps Between Spheres
Vladlen Timorin
Consider an analytic map of a neighborhood of 0 in a vector space to a Euclidean space. Suppose that this map takes all germs of lines passing through 0 to germs of circles. Such a…
Symplectic homology and periodic orbits near symplectic submanifolds
Kai Cieliebak, Viktor L. Ginzburg, Ely Kerman
We show that a small neighborhood of a closed symplectic submanifold in a geometrically bounded aspherical symplectic manifold has non-vanishing symplectic homology. As a consequen…
On uniqueness and differentiability in the space of Yamabe metrics
Michael T. Anderson
We prove that generically (positive) Yamabe metrics are unique in their conformal class, and describe some sufficient conditions which imply that a Yamabe metric of locally maximal…
An Algorithmic Study of Manufacturing Paperclips and Other Folded Structures
Esther M. Arkin, Sandor P. Fekete, Joseph S. B. Mitchell
We study algorithmic aspects of bending wires and sheet metal into a specified structure. Problems of this type are closely related to the question of deciding whether a simple non…
Cheeger-Gromov Theory and Applications to General Relativity
Michael T. Anderson
This paper surveys aspects of the convergence and degeneration of Riemannian metrics on a given manifold M - the Cheeger-Gromov theory - and extensions thereof to Ricci curvature i…