Related papers: Microlocalization and nonexistence of $C^2$ Levi-f…
This survey paper, aimed at nonexperts in the field, explores various proofs of nonexistence of real analytic Levi-flat hypersurfaces in $\mathbb CP^n$, $n>2$. Some generalizations and other related results are also discussed.
In this paper we prove the following theorem. Main Theorem. Let n >= 3 and m >= 3n/2 +7. Then there exists no C^m Levi-flat real hypersurface M in P_n. The condition that M is Levi-flat means that when M is locally defined by the vanishing…
This paper has been withdrawn by the author due to a crucial error in the proof of Lemma 2.2.
This paper has been withdrawn by the author due to a crucial sign error in Theorem 3.4.
This paper has been withdrawn because of serious errors.
This paper has been withdrawn by the author due to the gaps in the proofs of Proposition 2.2 and Proposition 3.2
This paper has been withdrawn by the author due to a crucial sign error in equation 1
The paper has been withdrawn due to a crucial error in section 3.
This paper has been withdrawn by the author due to crucial errors.
This paper has been withdrawn by the author, due to an important sign error in Eqn. 2.
This paper has been withdrawn by the authors, because of serious experimental problems.
This paper has been withdrawn by the author due to a mistake in the section 4.
We prove the existence of normal forms for some local real-analytic Levi-flat hypersurfaces with an isolated line singularity. We also give sufficient conditions for that a Levi-flat hypersurface with a complex line as singularity to be a…
Local conditions on boundaries of $C^\infty$ Levi-flat hypersurfaces, in case the boundary is a generic submanifold, are studied. For nontrivial real analytic boundaries we get an extension and uniqueness result, which forces the…
This paper has been withdrawn by the author due to a crucial sign error in Proposition 3.1.
This paper has been withdrawn because the new one gr-qc/0512095 includes all its results (as well as those in gr-qc/0511016) in a clearer way.
A Lipschitz hypersurface is a hypersurface which locally is the graph of a Lipschitz function. A Lipschitz (or C^1) hypersurface is said to be Levi-flat if it is locally foliated by complex manifolds of complex dimension (n-1). We shall…
This paper has been withdrawn due a crucial mistake due to a crucial mistake in the proof of Lemma 2.3.
This paper has been withdrawn by the author, due to errors in the figures.
This paper has been withdrawn by the author due to serious error found in main argument.