Displaying 21 – 40 of 864

Showing per page

Scalar differential invariants of symplectic Monge-Ampère equations

Alessandro Paris, Alexandre Vinogradov (2011)

Open Mathematics

All second order scalar differential invariants of symplectic hyperbolic and elliptic Monge-Ampère equations with respect to symplectomorphisms are explicitly computed. In particular, it is shown that the number of independent second order invariants is equal to 7, in sharp contrast with general Monge-Ampère equations for which this number is equal to 2. We also introduce a series of invariant differential forms and vector fields which allow us to construct numerous scalar differential invariants...

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...

Currently displaying 21 – 40 of 864