## Averaging of isotropic submanifolds

#### Marco ZambonUniversity of California at BerkeleyMathematics

Using an averaging procedure by Alan Weinstein and Moser's
trick'' we will give a construction to obtain canonically an
isotropic average of given $C^1$ close conpact isotropic submanifolds of a K\"ahler manifold. The isotropic average will be $C^0$ close to the given submanifolds, and the construction will be
equivariant with respect to K\"ahler diffeomorphisms.\\As a corollary we obtain that if an isotropic submanifold is almost invariant under an action by K\"ahler diffeomorphisms, then nearby there will be an invariant one.

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