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J.J. Green
J.J. Green
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I understand that little is known on the surface area of the unit ball in $\ell_p$, excepting the cases $p=1,2,\infty$, but can anything be said on the relation between the surface areas for $p$ and its conjugate $p'$? I'm particularly interested in small dimensions (up to five or so).

I seek invariants for tests for some code I have which estimates the surface area.

I understand that little is known on the surface area of the unit ball in $\ell_p$, excepting the cases $p=1,2,\infty$, but can anything be said on the relation between the surface areas for $p$ and its conjugate $p'$? I'm particularly interested in small dimensions (up to five or so).

I understand that little is known on the surface area of the unit ball in $\ell_p$, excepting the cases $p=1,2,\infty$, but can anything be said on the relation between the surface areas for $p$ and its conjugate $p'$? I'm particularly interested in small dimensions (up to five or so).

I seek invariants for tests for some code I have which estimates the surface area.

Source Link
J.J. Green
J.J. Green
  • 2.5k
  • 2
  • 20
  • 24

Relations between conjugate ℓₚ unit ball surface areas

I understand that little is known on the surface area of the unit ball in $\ell_p$, excepting the cases $p=1,2,\infty$, but can anything be said on the relation between the surface areas for $p$ and its conjugate $p'$? I'm particularly interested in small dimensions (up to five or so).