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.
Cite this article
Benoît Jubin, A Microlocal Characterization of Lipschitz Continuity. Publ. Res. Inst. Math. Sci. 54 (2018), no. 4, pp. 729–780DOI 10.4171/PRIMS/54-4-2