Kathleen A. Hoffman

The Bordered Operator and the Index of a Constrained Critical Point

L. Greenberg, J.H. Maddocks, and K.A. (Rogers) Hoffman


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.