Index formulas for higher order Loewner vector fields
نویسندگان
چکیده
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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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2010
ISSN: 0022-0396
DOI: 10.1016/j.jde.2010.06.026