Grom ov and Memarian (2003--2011) have established the waist inequality asserti ng that for any continuous map f from the sphere S^n to R^n-k there exists a fiber f^-1(y) such that every its t-neighborhood has measure at least the measure of the t-neighborhood of an equatorial subsphere S^k of S^n.Going to the limit we may say that the (n-k)-volume of the fiberf^-1(y) is at least that of the standard sphere S^k. We extend this limit statement to the exact bounds for balls in spaces of constant curva ture\, tori\, parallelepipeds\, projective spaces and other metric spaces. By the volume of preimages for a non-regular map f we mean its lower Minko wski content\, some new properties of which will be also presented in the talk.(based on the joint work with Roman Karasev and Alfredo Hubard)

LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS T Austria ORGANIZER:jdeanton@ist.ac.at SUMMARY:Waists of balls in different spaces URL:https://talks-calendar.app.ist.ac.at/events/1077 END:VEVENT END:VCALENDAR