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Potential Characterizations of Geodesic Balls on Hyperbolic Spaces: A Moving Plane Approach
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Potential Characterizations of Geodesic Balls on Hyperbolic Spaces: A Moving Plane Approach
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Journal Article
Potential Characterizations of Geodesic Balls on Hyperbolic Spaces: A Moving Plane Approach
2023
Overview
We consider the overdetermined problems in terms of the Riesz and Bessel potentials on hyperbolic space
H
n
. Taking advantage of the Helgason–Fourier analysis on the hyperbolic space, we apply the moving plane method in integral form to the corresponding integral equations and show that the solution is constant on the boundary of the domain if and only if the domain is a geodesic ball, and therefore, the solution is radially symmetric. Moreover, fractional-order equations involving the Laplace–Beltrami operator on the hyperbolic space are also considered by using their Green’s function estimates. Our operators also include the well-known GJMS operators on the hyperbolic space.
Publisher
Springer US,Springer Nature B.V
