The effect of curvature on convexity properties of harmonic functions and eigenfunctions (Q2840159)
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scientific article; zbMATH DE number 6188917
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The effect of curvature on convexity properties of harmonic functions and eigenfunctions |
scientific article; zbMATH DE number 6188917 |
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The effect of curvature on convexity properties of harmonic functions and eigenfunctions (English)
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17 July 2013
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eigenfunction
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curvature bound
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Riemannian manifold
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Laplacian operator
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nodal set
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harmonic function
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0.8988686
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0.8983243
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0.89427125
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0.88955104
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0.88807636
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0.8859234
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The author presents a simpler proof of the Donnelly and Fefferman growth bound for eigenfunctions (cf. \textit{H. Donnelly and C. Fefferman} [Invent. Math. 93, No. 1, 161--183 (1988; Zbl 0659.58047)]). Other previous simplifications on the original proof are also described in the present paper. Moreover, new quantitative geometric estimates in terms of curvature bounds are obtained.
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