Timeline for $\mathbb{CP}^1$-structures and hyperbolic Gauss maps
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jun 7, 2014 at 23:42 | comment | added | Misha | The paper to read is D.Dumas "Holonomy limits of complex projective structures". | |
| Jun 7, 2014 at 17:23 | comment | added | Xin Nie | Thanks, these are important informations. Now it seems to me that this map is not as good as I thought. B.T.W., the principal curvatures of the image of an harmonic map can be quite arbitrary. | |
| Jun 7, 2014 at 12:07 | comment | added | Lee Mosher | You might find the papers of Epstein and Marden interesting. Rather than consider $\phi(\Omega)$ and projecting that back to $\partial\mathbb{H}^3$, they consider the boundary of the $\mathbb{H}^3$ convex hull of $\Omega$, and they project that back to $\Omega$. They construct these maps to be uniformly quasiconformal. That might be a better, or at least easier, guess for $g \circ \phi$ than that it be conformal. | |
| Jun 7, 2014 at 11:00 | comment | added | user126154 | this does not answer the question, but may be of interest. By results of F. Labourie and G. Smith, (under some weak hypotheses on S) for every map $f:\tilde S\to\partial \mathbb H^3$ there is a unique map $\tilde S\to\mathbb H^3$ whose image is a surface of constant curvature and whose Gauss map is $f$. What can be said about the curvature of the image of an harmonic map? | |
| Jun 7, 2014 at 3:33 | history | edited | Ricardo Andrade |
replaced tag 'calculus-of-variations' with 'ap.analysis-of-pdes' (sorry to edit this question twice)
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| Jun 7, 2014 at 3:05 | history | edited | Ricardo Andrade |
replaced new tags with well-established ones, and added top-level tag: 'quasi-fuchsian-groups' --> 'dg.differential-geometry'; 'harmonic-maps' --> 'riemannian-geometry' and 'calculus-of-variations' (Please use well-established, general tags *before* using more specific tags or creating new ones)
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| Jun 6, 2014 at 19:47 | history | edited | Xin Nie |
edited tags
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| Jun 6, 2014 at 19:37 | history | edited | Xin Nie | CC BY-SA 3.0 |
added 16 characters in body
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| Jun 6, 2014 at 18:31 | history | edited | Xin Nie | CC BY-SA 3.0 |
added 59 characters in body
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| Jun 6, 2014 at 17:29 | history | asked | Xin Nie | CC BY-SA 3.0 |