Abstract
We investigate a potential with a radially symmetric and strictly decreasing kernel depending on a parameter. We regard the potential as a function defined on the upper half-space ℝm ×(0,+ ∞) and study some geometric properties of its spatial maximizer. To be precise, we give some sufficient conditions for the uniqueness of a maximizer of the potential and study the asymptotic behavior of the set of maximizers. Using these results, we imply geometric properties of some specific potentials. In particular, we consider applications for the solution of the Cauchy problem for the heat equation, the Poisson integral (including a solid angle) and rα-m-potentials.
| Original language | English |
|---|---|
| Pages (from-to) | 8347-8381 |
| Number of pages | 35 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 367 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 2015 Dec 1 |
Keywords
- Alexandrov's reflection principle
- Heart
- Hot spot
- Illuminating center
- Minimal unfolded region
- Moving plane method
- Newton potential
- Poisson integral
- R<sup>α-m</sup>-potential
- Radial center
- Riesz potential
- Solid angle
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
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Cite this
Sakata, S. (2015). Movement of centers with respect to various potentials. Transactions of the American Mathematical Society, 367(12), 8347-8381. https://doi.org/10.1090/tran/6138