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A New Proof Smooths Out the Math of Melting
A powerful mathematical technique is used to model melting ice and other phenomena. But it has long been imperiled by certain “nightmare scenarios.” A new proof has removed that obstacle.
To do so, they imagined an unusual shape — what Kleiner called “an evil catenoid.” It consists of two spheres, one inside the other, connected by a small cylinder, or neck, to form a single surface. In fact, Bamler and Kleiner showed that mean curvature flow almost always leads to one of two types of particularly simple singularities: spheres that shrink to a point, or cylinders that collapse to a line. Already, Chodosh added, the proof might allow mathematicians to use mean curvature flow to re-prove an important problem about symmetries of spheres, called the Smale conjecture.
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