The characterization problem of higher order rectifiable sets and a modelling problem for soap films are studied. In particular, necessary and sufficient geometric and quantitative conditions for a set to be rectifiable (in a higher order sense) are proved in Euclidean and metric spaces. Furthermore, a soap film model in the Euclidean plane is presented as a way to solving the Plateau problem in the plane.
Higher Order Rectifiability Criteria And a Model for Soap Films
2021
Abstract
The characterization problem of higher order rectifiable sets and a modelling problem for soap films are studied. In particular, necessary and sufficient geometric and quantitative conditions for a set to be rectifiable (in a higher order sense) are proved in Euclidean and metric spaces. Furthermore, a soap film model in the Euclidean plane is presented as a way to solving the Plateau problem in the plane.File in questo prodotto:
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Utilizza questo identificativo per citare o creare un link a questo documento:
https://hdl.handle.net/20.500.14242/141963
Il codice NBN di questa tesi è
URN:NBN:IT:UNIPI-141963