Approximation and convergence of formal CR-mappings

Details Approximation and convergence of formal CR-mappings Approximation and convergence of formal CR-mappings

2002-05-14

arxiv.org/abs/math/0205151v1

Mathematics

Complex Variables

Scientific paper

Let $M\subset C^N$ be a minimal real-analytic CR-submanifold and $M'\subset C^{N'}$ a real-algebraic subset through points $p\in M$ and $p'\in M'$. We show that that any formal (holomorphic) mapping $f\colon (C^N,p)\to (C^{N'},p')$, sending $M$ into $M'$, can be approximated up to any given order at $p$ by a convergent map sending $M$ into $M'$. If $M$ is furthermore generic, we also show that any such map $f$, that is not convergent, must send (in an appropriate sense) $M$ into the set $E'\subset M'$ of points of D'Angelo infinite type. Therefore, if $M'$ does not contain any nontrivial complex-analytic subvariety through $p'$, any formal map $f$ as above is necessarily convergent.

Affiliated with

Also associated with

No associations

Rating

Approximation and convergence of formal CR-mappings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Approximation and convergence of formal CR-mappings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Approximation and convergence of formal CR-mappings will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-652572