Open Math Notes

Resources and inspiration for math instruction and learning

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Welcome to AMS Open Math Notes, a repository of freely downloadable mathematical works hosted by the American Mathematical Society as a service to researchers, faculty and students. Open Math Notes includes:

  • Draft works including course notes, textbooks, and research expositions. These have not been published elsewhere and are subject to revision.
  • Items previously published in the Journal of Inquiry-Based Learning in Mathematics, a refereed journal
  • Refereed publications at the AMS

Visitors are encouraged to download and use any of these materials as teaching and research aids, and to send constructive comments and suggestions to the authors.

Open Math Notes Advisory Board:

  • Karen Vogtmann, Chair | University of Warwick
  • Tom Halverson | Macalester College
  • Andrew Hwang | College of the Holy Cross
  • Robert Lazarsfeld | Stony Brook University
  • Mary Pugh | University of Toronto


Michael Taylor
University of North Carolina
Reference #


Posted date
2021-10-13 09:48:01
Revised date
2021-10-13 10:26:22
Notes type
   Topics Course
   Research Monographs
      Harmonic Analysis
      Functional Analysis
      Geometric Analysis
   Differential Equations
      Linear Partial Differential Equations
      Stochastic Process

The Dirichlet-to-Neumann Map and Fractal Variants

These notes develop the study of the Dirichlet-to-Neumann map N, associated to a domain in a compact Riemannian manifold, in a variety of situations, starting with the classical case of smoothly bounded domains, then Lipschitz domains, then rougher finite perimeter domains, and finally more exotic cases, where the boundary has a fractal character. We consider the semigroup generated by -N, as a Markov semigroup, with novel properties in the fractal case.

Course Notes and Supplementary Material (PDF format)

TypeFile (Size)Date
Course notes v2 PDF (504K) 10/13/21