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COMPLEX SUBMANIFOLDS IN REAL HYPERSURFACES
한종규,Giuseppe Tomassini 대한수학회 2010 대한수학회지 Vol.47 No.5
Let M be a C∞ real hypersurface in Cn+1, n ¸ 1, locally given as the zero locus of a C∞ real valued function r that is defined on a neighborhood of the reference point P ∈ M. For each k = 1, . . . , n we present a necessary and sufficient condition for there to exist a complex manifold of dimension k through P that is contained in M, assuming the Levi form has rank n − k at P. The problem is to find an integral manifold of the real 1-form i□r on M whose tangent bundle is invariant under the complex structure tensor J. We present generalized versions of the Frobenius theorem and make use of them to prove the existence of complex submanifolds.
COMPLEX SUBMANIFOLDS IN REAL HYPERSURFACES
Han, Chong-Kyu,Tomassini, Giuseppe Korean Mathematical Society 2010 대한수학회지 Vol.47 No.5
Let M be a $C^{\infty}$ real hypersurface in $\mathbb{C}^{n+1}$, $n\;{\geq}\;1$, locally given as the zero locus of a $C^{\infty}$ real valued function r that is defined on a neighborhood of the reference point $P\;{\in}\;M$. For each k = 1,..., n we present a necessary and sufficient condition for there to exist a complex manifold of dimension k through P that is contained in M, assuming the Levi form has rank n - k at P. The problem is to find an integral manifold of the real 1-form $i{\partial}r$ on M whose tangent bundle is invariant under the complex structure tensor J. We present generalized versions of the Frobenius theorem and make use of them to prove the existence of complex submanifolds.
On defining functions and cores for unbounded domains I
Harz, T.,Shcherbina, N.,Tomassini, G. Springer 2017 Mathematische Zeitschrift Vol.286 No.3
<P>We show that every strictly pseudoconvex domain Omega with smooth boundary in a complex manifold M admits a global defining function, i.e., a smooth plurisubharmonic function phi : U -> Rdefined on an open neighbourhoodU subset of M of (Omega) over bar such that Omega = {phi < 0}, d phi not equal 0 on b Omega and phi is strictly plurisubharmonic near b Omega. We then introduce the notion of the core c(Omega) of an arbitrary domain Omega subset of M as the set of all points where every smooth and bounded from above plurisubharmonic function on Omega fails to be strictly plurisubharmonic. If Omega is not relatively compact in M, then in general c(Omega) is nonempty, even in the case whenMis Stein. It is shown that every strictly pseudoconvex domain Omega subset of M with smooth boundary admits a global defining function that is strictly plurisubharmonic precisely in the complement of c(Omega). We then investigate properties of the core. In particular, we prove that the core is always 1-pseudoconcave.</P>
Iavicoli, Sergio,Valenti, Antonio,Barillari, Caterina,Fortuna, Grazia,Boccuni, Valeria,Carnevale, Francesco,Riva, Michele A.,Kang, Seong-Kyu,Tomassini, Luigi Occupational Safety and Health Research Institute 2020 Safety and health at work Vol.11 No.2
Background: The aim of this study is to illustrate the historical role of the International Commission on Occupational Health (ICOH) congresses as an arena where national and international occupational medicine can dialogue and as the first example of scientific transferability of the research and prevention results that have had such an impact on global public health. Methods: We used the ICOH Heritage Repository, in which ICOH congress proceedings (from the first congress in Milan in 1906 to the last congress, held in Dublin in 2018), are organised in an orderly way, updated and easily accessible according to open access logic. Results: We describe studies by three physicians who submitted significant scientific work to ICOH congresses, one on the battle against ancylostomiasis (Volante, 1906), the second (Quarelli, 1928) on carbon disulphide poisoning, and the third (Viola, 1969) on the carcinogenicity of vinyl chloride monomer. Priority is given to Italian cases, on account of the authors' obvious familiarity with the issues. Conclusion: The visibility offered in ICOH conferences and their published proceedings has boosted the international spread of their findings, contributing to the scientific transferability of the research results and influencing the development of policies and prevention interventions that have had a great impact on global public health.