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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.