Geodesic
Curvature of Level Curves of Harmonic Functions
Canadian mathematical bulletin, Tome 26 (1983) no. 4, pp. 399-405

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If H is an arbitrary harmonic function defined on an open set Ω⊂C, then the curvature of the level curves of H can be strictly maximal or strictly minimal at a point of Ω. However, if Ω is a doubly connected domain bounded by analytic convex Jordan curves, and if H is harmonic measure of Ω with respect to the outer boundary of Ω, then the minimal curvature of the level curves of H is attained on the boundary of Ω.
DOI : 10.4153/CMB-1983-066-4
Mots-clés : 30C99, 30C45, Harmonic functions, level curves, curvature 
Ortel, Marvin; Schneider, Walter. Curvature of Level Curves of Harmonic Functions. Canadian mathematical bulletin, Tome 26 (1983) no. 4, pp. 399-405. doi: 10.4153/CMB-1983-066-4
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     title = {Curvature of {Level} {Curves} of {Harmonic} {Functions}},
     journal = {Canadian mathematical bulletin},
     pages = {399--405},
     year = {1983},
     volume = {26},
     number = {4},
     doi = {10.4153/CMB-1983-066-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-066-4/}
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