Abstract
Let be a smooth function of two variables , and for each positive integer , let be a symmetric tensor field of type defined by and a finitely many-valued one-dimensional distribution obtained from : for example, is the one-dimensional distribution defined by the gradient vector field of ; consists of two one-dimensional distributions obtained from one-dimensional eigenspaces of Hessian of . In the present paper, we shall study the behavior of around its isolated singularity in ways which appear in [1]--[4]. In particular, we shall introduce and study a conjecture which asserts that the index of an isolated singularity with respect to is not more than one.
Citation
Naoya ANDO. "A conjecture in relation to Loewner's conjecture." J. Math. Soc. Japan 57 (1) 1 - 20, January, 2005. https://doi.org/10.2969/jmsj/1160745810
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