Abstract
We prove some results on the geometry of the level sets of harmonic functions, particularly regarding their ‘oscillation’ and ‘pinching’ properties. These results allow us to tackle three recent conjectures due to De Carli and Hudson (Bull London Math Soc 42:83–95, 2010). Our approach hinges on a combination of local constructions, methods from differential topology and global extension arguments.
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Enciso, A., Peralta-Salas, D. Some geometric conjectures in harmonic function theory. Annali di Matematica 192, 49–59 (2013). https://doi.org/10.1007/s10231-011-0211-4
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DOI: https://doi.org/10.1007/s10231-011-0211-4