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Open Problems and New Directions for p-Modulus on Networks

  • Nathan Albin
  • Pietro Poggi-Corradini
Chapter
Part of the Springer INdAM Series book series (SINDAMS, volume 26)

Abstract

The notion of p-modulus was created, and continues to play a vital role, in complex analysis and geometric function theory. Here we give an overview of the theory of p-modulus on networks that we have been developing in recent years. The hope is not only to develop a flexible tool on networks that can be useful for practical applications, but also that the rich unfolding theory on network will eventually inform the classical theory on metric measure spaces, Euclidean spaces, and the complex plane. We end by offering three open problems that are purely network theory problems. To keep the paper self-contained, we have not included possible applications, both to practical problems and to more theoretic function theoretic problems. We leave those directions for another time.

Keywords

p-Modulus Blocking duality 

1991 Mathematics Subject Classification

90C35 

Notes

Acknowledgements

The authors are supported by NSF n. 1201427 and n. 1515810.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of MathematicsKansas State UniversityManhattanUSA

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