Publications of the Research Institute for Mathematical Sciences


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Volume 54, Issue 4, 2018, pp. 729–780
DOI: 10.4171/PRIMS/54-4-2

Published online: 2018-10-18

A Microlocal Characterization of Lipschitz Continuity

Benoît Jubin[1]

(1) Université Paris 6 Pierre et Marie Curie, France

We study continuous maps between diff erential manifolds from a microlocal point of view. In particular, we characterize the Lipschitz continuity of these maps in terms of the microsupport of the constant sheaf on their graph. Furthermore, we give lower and upper bounds on the microsupport of the graph of a continuous map and use these bounds to characterize strict di fferentiability in microlocal terms.

Keywords: Microlocal theory of sheaves, Lipschitz maps, Dini derivatives

Jubin Benoît: A Microlocal Characterization of Lipschitz Continuity. Publ. Res. Inst. Math. Sci. 54 (2018), 729-780. doi: 10.4171/PRIMS/54-4-2