Geodesic
Geometric Proofs of some Classical Results on Boundary Values for Analytic Functions
Canadian mathematical bulletin, Tome 37 (1994) no. 2, pp. 263-269

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In this note we are going to give a geometric proof, using the method of the extremal metric, of the following result of Beurling. For any analytic function f(z) in the unit disc Δ of the plane with a bounded Dirichlet integral, the set E on the boundary of the unit disc where the nontangential limits of f(z) do not exist has logarithmic capacity zero. Also, using an unpublished result of Beurling, we will prove different results on boundary values for different classes of functions.
DOI : 10.4153/CMB-1994-038-x
Mots-clés : 30C45, Areally mean p-valent, extremal metric, logarithmic capacity 
Villamor, Enrique. Geometric Proofs of some Classical Results on Boundary Values for Analytic Functions. Canadian mathematical bulletin, Tome 37 (1994) no. 2, pp. 263-269. doi: 10.4153/CMB-1994-038-x
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     title = {Geometric {Proofs} of some {Classical} {Results} on {Boundary} {Values} for {Analytic} {Functions}},
     journal = {Canadian mathematical bulletin},
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     year = {1994},
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     doi = {10.4153/CMB-1994-038-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-038-x/}
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