Timeline for Integral of Gaussian curvature multiplied by mean curvature
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Nov 1, 2017 at 9:15 | comment | added | Ali Taghavi | For a possible related question please see mathoverflow.net/questions/240346/… | |
| Oct 5, 2017 at 5:19 | comment | added | Paul Bryan | If you have a variation $S_t$ of $S$ with normal speed $V$, then $\partial_t \operatorname{Area}(S) = -\int H V dS$. So $\int_S KH dS$ is (minus) the variation of area under the Gauss curvature flow. | |
| Oct 3, 2017 at 19:44 | comment | added | Willie Wong | If there is a good interpretation it would be specifically in the context of GR. Is the factor multiplied by any normalization constants (like total area?) Knowing exactly how the quantity scales can bring in some dimensional analysis arguments for the physical interpretation. Of course, it may possibly more obvious if you can just show us where this term comes up exactly. | |
| Oct 3, 2017 at 19:41 | comment | added | Willie Wong | There certainly cannot be a topological interpretation, as your expression depends on the extrinsic curvature, and is not scale invariant for round spheres in $\mathbb{R}^3$. Mean curvature is also only defined up to sign (choice of normal). | |
| Oct 3, 2017 at 14:20 | comment | added | Josh Kirklin | I'm studying apparent horizons ($S$) in general relativity. These are codimension-2 surfaces in a pseudo-Riemannian 4-manifold whose second fundamental forms are traceless. In a canonical Hamiltonian formalism, observable physical quantities are defined on a 3-dimensional Cauchy surface (which is $M$ here). Taking the Poisson bracket of two easy to physically interpret quantities gives me this integral, the physical interpretation of which I would like to ascertain. | |
| Oct 3, 2017 at 14:15 | history | edited | Josh Kirklin | CC BY-SA 3.0 |
specified spherical topology
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| Oct 3, 2017 at 14:12 | comment | added | Igor Rivin | Why do you ask? Where does this quantity come from? | |
| Oct 3, 2017 at 13:56 | history | edited | Martin Sleziak | CC BY-SA 3.0 |
removed deprecated (geometry) tag - see the tag info: http://mathoverflow.net/tags/geometry/info; if there are some other geometry-related tags which are suitable, please use some of them instead
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| Oct 3, 2017 at 13:39 | history | asked | Josh Kirklin | CC BY-SA 3.0 |