Talk:Systolic geometry: Difference between revisions

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I do not quite understand the figure and the caption. Is this the systole of the surface? Is it important that its a geodesic? --Salix alba (talk) 17:08, 25 April 2007 (UTC)[reply]

I am not sure Katzmik is aware of article talk pages. You may want to ask him directly on his own talk page about this. Oleg Alexandrov (talk) 02:38, 26 April 2007 (UTC)[reply]

I will try to include additional comments eventually. Essentially it illustrates a result of J. Hersch from 1955, which we used recently to prove Gromov's filling area conjecture. -MK

I have added some comments for now, in the section "filling area conjecture". Katzmik (talk) 12:37, 11 April 2008 (UTC)[reply]

Katzmik (talk · contribs) put this article into Category:Geometry stubs. I changed that to use the "geometry-stub" template instead. However, I think that this article may have already grown beyond the stub stage, so neither may be more appropriate. JRSpriggs 09:22, 3 May 2007 (UTC)[reply]

That's fine, whatever seems more appropriate by wiki standards. Should we delete both? Katzmik 10:53, 3 May 2007 (UTC)[reply]

Systolic mathematics appears to mesh well with a medical understanding of an anatomic/physiologic suspended sphere of muscle pumping blood through four fixed vectors heart valves in four distinct quadrants for +/- 72 years. Medical appreciation of the performance of the sphere is perhaps best appreciated mathematically in volumetric terms. Prior work by Adolph Fick in Cardiac Output readily applies terms to output/work of the heart. Contemporary adaptation of this work is understood as the Ejection Fraction of the heart and is very important in appreciation of Systolic Heart Failure. —Preceding unsigned comment added by Lbeben (talk • contribs) 02:51, 18 December 2008 (UTC)[reply]

The article defines a systole as follows:

"The systole of a compact metric space X is a metric invariant of X, defined to be the least length of a noncontractible loop in X (i.e. a loop that cannot be contracted to a point in the ambient space X)."

This definition omits the crucial fact that a systole makes sense only for a metric space that is not simply connected. (There is no minimum over the empty set.) The more technical definition that follows does likewise. Shouldn't it be made clear what class of spaces "systole" makes sense for?Daqu (talk) 22:14, 23 February 2009 (UTC)[reply]

I ran into problems while creating the category, and now am unable to move the article back to Systolic geometry. Tkuvho (talk) 13:40, 24 January 2010 (UTC)[reply]

 Done. Seemed uncontroversial enough. Jafeluv (talk) 14:37, 24 January 2010 (UTC)[reply]

Need to clarify relationship to Sub-Riemannian geometry which is also about isoperimetric stuff; the textbook I read long ago also appealed to some biblical example of putting up a fence to enclose some area. It then launched into non-holonomic constraints, which are entirely absent from this article -- maybe that's the big difference... 67.198.37.16 (talk) 21:41, 3 November 2020 (UTC)[reply]