منابع مشابه
An Index Formula for Loewner Vector Fields
Let f be C2 real-valued function defined near 0 in R2, ∂2f ∂z2 6= 0 for z 6= 0. Motivated by the Carathéodory conjecture in differential geometry, Loewner conjectured that the index at 0 of the vector field given in complex notation by ∂ 2f ∂z2 is at most two. In this paper we establish a formula that computes the index of these Loewner vector fields from data about the hessian of f .
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Let D be a Dirac type operator on a compact manifold M and let Σ be a Lipschitz submanifold of codimension one partitioningM into two Lipschitz domains Ω±. Also, let Hp±(Σ, D) be the traces on Σ of the (Lpstyle) Hardy spaces associated with D in Ω±. Then (Hp−(Σ, D),Hp+(Σ, D)) is a Fredholm pair of subspaces for Lp(Σ) (in Kato’s sense) whose index is the same as the index of the Dirac operator D...
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 2005
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2004.10.008