اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدEmbedded surfaces and almost complex structures
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Christian Bohr
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We prove necessary and sufficient conditions for a smooth surface in a 4-manifold X to be pseudoholomorphic with respect to some almost complex structure on X. This provides a systematic approach to the construction of pseudoholomorphic curves that do not minimize the genus in their homology class.
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In this paper we consider the existence and regularity of weakly polyharmonic almost complex structures on a compact almost Hermitian manifold $M^{2m}$. Such objects satisfy the elliptic system weakly $[J, Delta^m J]=0$. We prove a very general regul
arity theorem for semilinear systems in critical dimensions (with emph{critical growth nonlinearities}). In particular we prove that weakly biharmonic almost complex structures are smooth in dimension four.
We study the existence and regularity of energy-minimizing harmonic almost complex structures. We have proved results similar to the theory of harmonic maps, notably the classical results of Schoen-Uhlenbeck and recent advance by Cheeger-Naber.
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We introduce the notion of emph{biharmonic almost complex structure} on a compact almost Hermitian manifold and we study its regularity and existence in dimension four. First we show that there always exist smooth energy-minimizing biharmonic almost
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