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A note on nodal sets on manifolds with lower Ricci bound (Q820863)

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scientific article; zbMATH DE number 7402082
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English
A note on nodal sets on manifolds with lower Ricci bound
scientific article; zbMATH DE number 7402082

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    A note on nodal sets on manifolds with lower Ricci bound (English)
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    28 September 2021
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    As the authors point out, ``the study of nodal sets for solutions and eigenfunctions is very important for understanding geometric properties of elliptic operators.'' In this paper the authors initiate the study of uniform measure estimates for nodal sets of harmonic functions \(u\) on a Riemannian manifold \((M, g)\) with lower Ricci curvature, which leads to lower regularity of the solution \(u\). The paper has a first introductory section where the main result is stated and two other sections: one with the proof of the upper bound estimate in the main theorem and another one with the proof of the lower bound estimate. The authors add three appendixes with some previously used results that make the paper quite self-contained.
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    nodal sets
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    lower Ricci curvature
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    noncollapsing
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    uniform measure estimates
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