Generalized versions of Ilmanen lemma: Insertion of or functions
Václav Kryštof (2018)
Commentationes Mathematicae Universitatis Carolinae
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We prove that for a normed linear space , if is continuous and semiconvex with modulus , is continuous and semiconcave with modulus and , then there exists such that . Using this result we prove a generalization of Ilmanen lemma (which deals with the case ) to the case of an arbitrary nontrivial modulus . This generalization (where a function is inserted) gives a positive answer to a problem formulated by A. Fathi and M. Zavidovique in 2010.