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.
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Acknowledgements
The authors are supported by NSF n. 1201427 and n. 1515810.
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Albin, N., Poggi-Corradini, P. (2017). Open Problems and New Directions for p-Modulus on Networks. In: Bracci, F. (eds) Geometric Function Theory in Higher Dimension. Springer INdAM Series, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-73126-1_10
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