Publications of the Research Institute for Mathematical Sciences
Full-Text PDF (700 KB) | Metadata | Table of Contents | PRIMS summary
Published online: 2018-10-18
A Microlocal Characterization of Lipschitz ContinuityBenoît Jubin (1) Université Paris 6 Pierre et Marie Curie, France
We study continuous maps between differential 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 differentiability 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