For a C^{1,1} function whose Hessian has uniformly positive or negative determinant almost everywhere, the index of the Hessian is constant almost everywhere, proving Šverák's 1992 conjecture.
Chang.Infinite Dimensional Morse Theory and Multiple Solution Problems
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Constancy of the index for gradient mappings
For a C^{1,1} function whose Hessian has uniformly positive or negative determinant almost everywhere, the index of the Hessian is constant almost everywhere, proving Šverák's 1992 conjecture.