Formal biholomorphic maps of real-analytic hypersurfaces
Mir, Nordine
HAL, hal-00261679 / Harvested from HAL
Text on HAL
Let $f : (M,p) \rightarrow (M',p')$ be a formal biholomorphic mapping between two germs of real analytic hypersurfaces in $\C^n$, $p'=f(p)$. Assuming the source manifold to be minimal at $p$, we prove the convergence of the so-called reflection function associated to $f$. As a consequence, we derive the convergence of formal biholomorphisms between real analytic minimal holomorphically nondegenerate hypersurfaces. Related results on partial convergence of formal biholomorphisms are also obtained.
Publié le : 2000-05-05
Classification:  Artin approximation theorem,  Formal mapping,  Real analytic hypersurfaces,  Holomorphic nondegeneracy,  Cauchy estimates,  Artin approximation theorem.,  1999 AMS: 32C16, 32H02, Secondary 32H99,  [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV] 
@article{hal-00261679,
     author = {Mir, Nordine},
     title = {Formal biholomorphic maps of real-analytic hypersurfaces},
     journal = {HAL},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00261679}
}

Mir, Nordine. Formal biholomorphic maps of real-analytic hypersurfaces. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-00261679/