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+proof
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Anton Petrunin
Anton Petrunin
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  • There is no path isometry $\mathbb R^2\to\mathbb R$ (search for length-preserving map in my collection);
  • There is no path isometry $(\mathbb R^2,\ell_p)\to\mathbb R^n$ for $p\not=2$.
  • There is no path isometry $\mathbb R^2\to\mathbb R$;
  • There is no path isometry $(\mathbb R^2,\ell_p)\to\mathbb R^n$ for $p\not=2$.
  • There is no path isometry $\mathbb R^2\to\mathbb R$ (search for length-preserving map in my collection);
  • There is no path isometry $(\mathbb R^2,\ell_p)\to\mathbb R^n$ for $p\not=2$.
Source Link
Anton Petrunin
Anton Petrunin
  • 45k
  • 14
  • 135
  • 299

  • There is no path isometry $\mathbb R^2\to\mathbb R$;
  • There is no path isometry $(\mathbb R^2,\ell_p)\to\mathbb R^n$ for $p\not=2$.