• Corpus ID: 235294028

Two-dimensional metric spheres from gluing hemispheres

  title={Two-dimensional metric spheres from gluing hemispheres},
  author={Toni Ikonen},
We study metric spheres (Z, dZ) obtained by gluing two hemispheres of S2 along an orientation-preserving homeomorphism g : S1 → S1, where dZ is the canonical distance that is locally isometric to S2 off the seam. We show that if (Z, dZ) is quasiconformally equivalent to S 2, in the geometric sense, then g is a welding homeomorphism with conformally removable welding curves. We also show that g is bi-Lipschitz if and only if (Z, dZ) has a 1quasiconformal parametrization whose Jacobian is… 
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