Supersqueezed surfaces

Series
Geometry Topology Seminar
Time
Monday, September 21, 2026 - 2:00pm for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hongda Qiu – Georgia Tech
Organizer
John Etnyre

We discuss a new problem by Dmitri Burago and Anton Petrunin. Consider a $C^2$-smooth surface embedded in $\RR^3$ with principal curvatures $\leq 1$. Does such a surface necessarily enclose a volume at least that of the unit ball? We address results from two opposite perspectives: On the one hand, we can construct a counterexample by deforming Lagunov's fishbowl (a fattened Bing's house); on the other hand, there are positive results with additional conditions. Many problems remain open.