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The Bordered Operator and the Index, of a Constrained Critical Point
Author(s) -
Greenberg Leon,
Maddocks John H.,
Hoffman Kathleen A.
Publication year - 2000
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200011)219:1<109::aid-mana109>3.0.co;2-1
Subject(s) - mathematics , isoperimetric inequality , operator (biology) , critical point (mathematics) , eigenvalues and eigenvectors , point (geometry) , conjugate points , index (typography) , pure mathematics , mathematical analysis , geometry , biochemistry , chemistry , physics , repressor , quantum mechanics , world wide web , computer science , transcription factor , gene
It is shown that the index of a constrained critical point in the isoperimetric calculus of variations is simply related to the number of negative eigenvalues of a certain bordered operator associated with the second variation. A conjugate point theory for this bordered operator is then established.