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EIGENVALUE ESTIMATES AND THE INDEX OF HESSIAN FIELDS

Published online by Cambridge University Press:  18 April 2001

BRIAN SMYTH  and
FREDERICO XAVIER
BRIAN SMYTH
Affiliation:
Mathematics Department, University of Notre Dame, Notre Dame, IN 46556, USA; e-mail: smyth.1@nd.edu, xavier.1@nd.edu
FREDERICO XAVIER
Affiliation:
Mathematics Department, University of Notre Dame, Notre Dame, IN 46556, USA; e-mail: smyth.1@nd.edu, xavier.1@nd.edu
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Abstract

The local Caratheodory conjecture on the index of an isolated singularity of the principal foliations in surface theory is equivalent to a conjecture of Loewner on the index of the isolated singularities of the Hessian operator of a smooth function in the plane. Here we prove the latter conjecture for a special class of functions.

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Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 1 , January 2001 , pp. 109 - 112
Copyright
© The London Mathematical Society 2001

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