This paper introduces a geometric, potential theoretic approach to the study of twist point in the boundary of a planar domain. It introduces a map h from a domain D to harmonic functions such that, when z tends to a boundary point w, the limit behaviour of h determines if w is a twist point or is sectorially accessible. The construction is based only on potential-theoretic methods and does not use the Riemann mapping theorem.

Arcozzi, N., Casadio-Tarabusi, E., Di Biase, F., & Picardello, A.M. (2005). A potential theoretic approach to twisting. In D. Bakry, L. Beznea, G. Bucur, & M. Rockner (a cura di), Current trends in potential theory (pp. 3-15). Bucarest : Theta Foundation.

A potential theoretic approach to twisting

PICARDELLO, ANGELO MASSIMO
2005

Abstract

This paper introduces a geometric, potential theoretic approach to the study of twist point in the boundary of a planar domain. It introduces a map h from a domain D to harmonic functions such that, when z tends to a boundary point w, the limit behaviour of h determines if w is a twist point or is sectorially accessible. The construction is based only on potential-theoretic methods and does not use the Riemann mapping theorem.
Settore MAT/05 - Analisi Matematica
eng
Rilevanza internazionale
Capitolo o saggio
Twist point; sectorially accessible; Riemann mapping; McMillan theorem; NTA domains
The editorial placement is misleading: this was the first paper where a purely potential-theoretical approach was developed to classify twist point of planar domains. The Riemann mapping theorem is not used! This opens the way to extend this type of results to higher dimensions, a very challenging problem.
Arcozzi, N., Casadio-Tarabusi, E., Di Biase, F., & Picardello, A.M. (2005). A potential theoretic approach to twisting. In D. Bakry, L. Beznea, G. Bucur, & M. Rockner (a cura di), Current trends in potential theory (pp. 3-15). Bucarest : Theta Foundation.
Arcozzi, N; Casadio Tarabusi, E; Di Biase, F; Picardello, Am
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/55445
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