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Genericity of Nondegenerate Critical Points and Morse Geodesic Functionals
(INDIANA UNIV MATH JOURNAL, 2009)
We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Using classical ...
GENERICITY OF NONDEGENERATE GEODESICS WITH GENERAL BOUNDARY CONDITIONS
(JULIUSZ SCHAUDER CTR NONLINEAR STUDIES, 2010)
Let M be a possibly noncompact manifold. We prove, generically in the C(k)-topology (2 <= k <= infinity), that semi-Riemannian metrics of a given index on M do not possess any degenerate geodesics satisfying suitable ...