Skip to main content
Mohammad Ghomi's user avatar
Mohammad Ghomi's user avatar
Mohammad Ghomi's user avatar
Mohammad Ghomi
  • Member for 9 years, 9 months
  • Last seen this week
awarded
revised
Loading…
Loading…
comment
Contractibility of the space of Jordan curves
@Pierre PC: Continuous dependence on prescribed boundary data follows from Caratheodory's kernel theorem, which gives conditions for local uniform convergence of conformal maps. See "Boundary Behavior of Conformal maps" by Pommerenke; specifically, Thm. 2.11 which Pommerenke attributes to Rado. This takes care of continuous dependence on a single boundary component. The case of multiple boundary components should be very similar, since the arguments are local.
awarded
awarded
awarded
revised
Loading…
revised
Contractibility of the space of Jordan curves
added 25 characters in body
Loading…
revised
Contractibility of the space of Jordan curves
deleted 34 characters in body
Loading…
revised
Contractibility of the space of Jordan curves
added 135 characters in body
Loading…
comment
Contractibility of the space of Jordan curves
@ Mikhail Katz: I don't know the best reference for CSF for polygons, but Carpenter's rule problem has been well studied in the paper of Connelly, Demaine and Rote.
comment
Contractibility of the space of Jordan curves
@ Mikhail Katz: Curve shortening flow works for polygonal curves as well, and there are also other methods like the "Carpenter Rule Problem" which convexifies polygons in a canonical way.
revised
Contractibility of the space of Jordan curves
deleted 1 character in body
Loading…
revised
Contractibility of the space of Jordan curves
deleted 10 characters in body
Loading…
revised
Contractibility of the space of Jordan curves
deleted 39 characters in body
Loading…
revised
Contractibility of the space of Jordan curves
deleted 42 characters in body
Loading…
revised
Contractibility of the space of Jordan curves
deleted 19 characters in body
Loading…
revised
Loading…
revised
Contractibility of the space of Jordan curves
deleted 2 characters in body
Loading…
1
6 7
8
9 10
37