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Bulletin of the London Mathematical Society 2001 33(1):109-112; doi:10.1112/blms/33.1.109
© 2001 by London Mathematical Society
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© London Mathematical Society

Eigenvalue Estimates and the Index of Hessian Fields

Brian Smyth and Frederico Xavier

Mathematics Department, University of Notre Dame Notre Dame, IN 46556, USA; e-mail: smyth.1{at}nd.edu, xavier.1{at}nd.edu

Received 18 June 1999. Revision received 21 February 2000.

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.

The work of both authors was partially supported by NSF grants.


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