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Schiffer problem and isoparametric hypersurfaces.

Vladimir E. Shklover (2000)

Revista Matemática Iberoamericana

The Schiffer Problem as originally stated for Euclidean spaces (and later for some symmetric spaces) is the following: Given a bounded connected open set Ω with a regular boundary and such that the complement of its closure is connected, does the existence of a solution to the Overdetermined Neumann Problem (N) imply that Ω is a ball? The same question for the Overdetermined Dirichlet Problem (D). We consider the generalization of the Schiffer problem to an arbitrary Riemannian manifold and also...

Second order connections on some functional bundles

Antonella Cabras, Ivan Kolář (1999)

Archivum Mathematicum

We study the second order connections in the sense of C. Ehresmann. On a fibered manifold Y , such a connection is a section from Y into the second non-holonomic jet prolongation of Y . Our main aim is to extend the classical theory to the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base. This requires several new geometric results about the second order connections on Y , which are deduced in the first part of the paper.

Seiberg-Witten Theory

Jürgen Eichhorn, Thomas Friedrich (1997)

Banach Center Publications

We give an introduction into and exposition of Seiberg-Witten theory.

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