Timeline for What is the definition of "geometric analysis"? [closed]
Current License: CC BY-SA 3.0
15 events
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| Jan 29, 2019 at 20:55 | comment | added | Zhiqiang Sun | But generally speaking you can also call all the analytical methods appearing in differential/ algebraic geometry the method of "geometric analysis", but this is not the common definition of GA. | |
| Jan 29, 2019 at 20:52 | comment | added | Zhiqiang Sun | 1. Prescribing canonical metrics with specified curvature conditions, for example the classical Yamabe problem, prescribing constant Ricci curvature in Kähler geometry(Kähler Einstein metrics) 2. Geometric variational problem, for example, the study of minimal surfaces, Willmore conjecture, harmonic maps. 3. Geometric evolution equations, for example, the Ricci flow, Kähler Ricci flow. | |
| Jan 29, 2019 at 20:46 | comment | added | Zhiqiang Sun | In my opinion, in the narrow sense the "Geometric Analysis" is a collection of mathematical methods/ problems of the following three types: | |
| May 14, 2018 at 22:41 | review | Reopen votes | |||
| May 15, 2018 at 1:13 | |||||
| May 14, 2018 at 22:28 | comment | added | Piotr Hajlasz | I think it is a very good question. The "official" definition of geometric analysis pointed out by Willie Wong is not necessarily what many people think geometric analysis really is. I think my research is in geometric analysis, but I never dare to mention geometric analysis in my NSF proposals, because I do not want to be placed in the panel mentioned by Willie Wong. I always end up in the "Geometric Function Theory" panel, although I really think my research should be called "Geometric Analysis". I think a honest discussion about meaning of geometric analysis would be a good thing to do. | |
| May 1, 2017 at 16:07 | comment | added | Zhexiu Tu | @RyanBudney: I mean something written down as "Definition:....". You can define PDE to be the subject related to solving partial differential equations. I do not know how to define geometric analysis. | |
| Apr 28, 2017 at 12:45 | history | closed |
Ryan Budney Stefan Waldmann Neil Strickland Stefan Kohl♦ Chris Godsil |
Needs details or clarity | |
| Apr 28, 2017 at 9:05 | comment | added | Helene Sigloch | I hardly believe that "the subject partial differential equations" or "the subject algebraic geometry" are well-defined. It always depends on your point of view. For example, is arithmetic geometry part of algebraic geometry or of number theory? Many areas of research are in the intersection of different subjects and if person A tells you that person B is doing algebraic geometry, this tells you almost as much about person A as about person B. Therefore I think that the best you can hope for is a list of descriptions of what people think geometric analysis is, not an objective definition. | |
| Apr 28, 2017 at 7:23 | history | edited | Mikhail Katz |
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| Apr 28, 2017 at 4:36 | comment | added | Ryan Budney | Your question is somewhat ill-defined. What do you mean by "subject" and "well-defined"? Clearly geometric analysis makes enough sense to the people that use the term. If you articulate more clearly what it is you are looking for, perhaps people can help you. | |
| Apr 28, 2017 at 3:05 | history | edited | Willie Wong |
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| Apr 28, 2017 at 3:04 | comment | added | Willie Wong | for the pragmatic minded, there is a good enough definition :-) | |
| Apr 28, 2017 at 2:47 | review | Close votes | |||
| Apr 28, 2017 at 12:45 | |||||
| Apr 28, 2017 at 2:31 | review | First posts | |||
| Apr 28, 2017 at 2:35 | |||||
| Apr 28, 2017 at 2:26 | history | asked | Zhexiu Tu | CC BY-SA 3.0 |