Timeline for H-principle and PDE's
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Mar 12, 2017 at 14:40 | history | edited | Willie Wong |
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| Feb 18, 2012 at 22:15 | vote | accept | Pawel | ||
| Feb 17, 2012 at 3:13 | answer | added | Phil Isett | timeline score: 18 | |
| Feb 16, 2012 at 18:46 | answer | added | Igor Khavkine | timeline score: 4 | |
| Feb 16, 2012 at 8:46 | comment | added | Willie Wong | Another good place to look (I have to thank Igor Khavkine for pointing it out to me) is David Spring's Convex Integration Theory. I have some difficulty following the writing styles of Gromov or Eliashberg-Mishachev; Spring is slightly easier to read for me. | |
| Feb 15, 2012 at 21:13 | answer | added | Elizabeth S. Q. Goodman | timeline score: 10 | |
| Feb 15, 2012 at 20:49 | answer | added | alvarezpaiva | timeline score: 12 | |
| Feb 15, 2012 at 20:38 | answer | added | Jonny Evans | timeline score: 27 | |
| Feb 15, 2012 at 16:18 | comment | added | j.c. | I second Marco Golla's recommendation, though the introduction is called an "Intrigue" in that book. The Overview lecture from John Francis's course also gives a nice set of examples: math.northwestern.edu/~jnkf/classes/hprin | |
| Feb 15, 2012 at 14:48 | comment | added | Marco Golla | I'd consider taking a look at Eliashberg and Mishachev's "Introduction to the h-principle" (or at least its introduction/table of contents). | |
| Feb 15, 2012 at 13:47 | comment | added | Deane Yang | I'm not any more of an expert than Paul, so here's another vague comment: My impression from looking at Gromov's book is that the h-principle is useful only when there are a lot of solutions to the system of PDE's. This occurs when either the PDE is really a PDI (partial differential inequality) or a sufficiently underdetermined system of PDE's. Gromov, for example, proves lots of isometric embedding theorems but only in sufficiently high codimension (even then his results are better than most other results in this area). The h-principle has also been used a lot in symplectic geometry. | |
| Feb 15, 2012 at 13:37 | comment | added | Paul Siegel | I'm told that it is not of very much interest to PDE theorists, who are often concerned with rigidity and regularity phenomena. | |
| Feb 15, 2012 at 13:36 | comment | added | Paul Siegel | I'm nowhere near an expert so I'm only going to leave a comment. What I know about the h-principle is that it is a sweeping generalization of the implicit function theorem in the sense that it reduces existence questions about nonlinear PDEs to existence questions about algebraic equations. It is generally applicable to problems in geometry where you want to show that some complicated geometric procedure is possible (such as continuously inverting a sphere or smoothly embedding one manifold into another) but you aren't too concerned with regularity issues. | |
| Feb 15, 2012 at 12:34 | history | asked | Pawel | CC BY-SA 3.0 |