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A concavity condition for existence of a negative value in Neumann-Poincaré spectrum in three dimensions


Authors: Yong-Gwan Ji and Hyeonbae Kang
Journal: Proc. Amer. Math. Soc. 147 (2019), 3431-3438
MSC (2010): Primary 47A45; Secondary 31B25
DOI: https://doi.org/10.1090/proc/14467
Published electronically: April 3, 2019
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Abstract: It is proved that if a bounded domain in three dimensions satisfies a certain concavity condition, then the Neumann-Poincaré operator on either the boundary of the domain or its inversion in a sphere has a negative value in its spectrum. The concavity condition is quite simple, and is satisfied if there is a point on the boundary at which the Gaussian curvature is negative.


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Additional Information

Yong-Gwan Ji
Affiliation: Department of Mathematics, Inha University, Incheon 22212, South Korea
Email: 22151063@inha.edu

Hyeonbae Kang
Affiliation: Department of Mathematics, Inha University, Incheon 22212, South Korea
Email: hbkang@inha.ac.kr

DOI: https://doi.org/10.1090/proc/14467
Received by editor(s): September 12, 2018
Received by editor(s) in revised form: November 12, 2018
Published electronically: April 3, 2019
Additional Notes: This work was supported by the National Research Foundation of Korea through grants No. 2016R1A2B4011304 and 2017R1A4A1014735.
Communicated by: Michael Hitrik
Article copyright: © Copyright 2019 American Mathematical Society