arXiv
Open Access
2021
Minimizing capacity among linear images of rotationally invariant conductors
Richard S. Laugesen
Abstrak
Logarithmic capacity is shown to be minimal for a planar set having $N$-fold rotational symmetry ($N \geq 3$), among all conductors obtained from the set by area-preserving linear transformations. Newtonian and Riesz capacities obey a similar property in all dimensions, when suitably normalized linear transformations are applied to a set having irreducible symmetry group. A corollary is Pólya and Schiffer's lower bound on capacity in terms of moment of inertia.
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Richard S. Laugesen
Akses Cepat
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- Tahun Terbit
- 2021
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