Eigenvalue Estimates and the Index of Hessian Fields | Zendy

Smyth Brian | Zendy; Xavier Frederico | Zendy

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Eigenvalue Estimates and the Index of Hessian Fields

Author(s) -

Smyth Brian,

Xavier Frederico

Publication year - 2001

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms/33.1.109

Subject(s) - mathematics , conjecture , hessian matrix , gravitational singularity , index (typography) , eigenvalues and eigenvectors , singularity , pure mathematics , operator (biology) , hessian equation , mathematical analysis , function (biology) , class (philosophy) , principal (computer security) , plane (geometry) , geometry , differential equation , first order partial differential equation , world wide web , computer science , quantum mechanics , physics , repressor , artificial intelligence , chemistry , biology , operating system , biochemistry , evolutionary biology , transcription factor , gene

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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