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RISS 인기검색어
- 검색키워드
- 저자 : Harz, J. (검색결과 3 건)
- 무료
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- 유료
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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>
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On the Dimension of the Bergman Space for Some Unbounded Domains
Gallagher, A. K.,Harz, T.,Herbort, G. MATHEMATICA JOSEPHINA, INC 2017 JOURNAL OF GEOMETRIC ANALYSIS Vol.27 No.2
<P>A sufficient condition for the infinite dimensionality of the Bergman space of a pseudoconvex domain is given. This condition holds on any pseudoconvex domain that has at least one smooth boundary point of finite type in the sense of D'Angelo.</P>
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Chun, E. J.,Cvetič,, G.,Dev, P. S. B.,Drewes, M.,Fong, C. S.,Garbrecht, B.,Hambye, T.,Harz, J.,Herná,ndez, P.,Kim, C. S.,Molinaro, E.,Nardi, E.,Racker, J.,Rius, N.,Zamora-Saa, J. World Scientific Publishing Company 2018 International journal of modern physics. A, Partic Vol.33 No.6
<P>The focus of this paper lies on the possible experimental tests of leptogenesis scenarios. We consider both leptogenesis generated from oscillations, as well as leptogenesis from out-of-equilibrium decays. As the Akhmedov-Rubakov-Smirnov (ARS) mechanism allows for heavy neutrinos in the GeV range, this opens up a plethora of possible experimental tests, e.g. at neutrino oscillation experiments, neutrinoless double beta decay, and direct searches for neutral heavy leptons at future facilities. In contrast, testing leptogenesis from out-of-equilibrium decays is a quite difficult task. We comment on the necessary conditions for having successful leptogenesis at the TeV-scale. We further discuss possible realizations and their model specific testability in extended seesaw models, models with extended gauge sectors, and supersymmetric leptogenesis. Not being able to test high-scale leptogenesis directly, we present a way to falsify such scenarios by focusing on their washout processes. This is discussed specifically for the left-right symmetric model and the observation of a heavy <TEX>$ W_{R}$</TEX>, as well as model independently when measuring <TEX>$ \Updelta L = 2$</TEX> washout processes at the LHC or neutrinoless double beta decay.</P>
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