Mathematicians have proven a long -raised problem in the area of geometry that studies all forms that can have an ice cube melting.
To model the melting of ice and other phenomena, mathematicians use Mathematical technique of the defrost. The goal is to understand how the ice surface changes over the time it melts. It’s all about, therefore, with geometry.
In this process, mathematicians use a process called medium curvature flow, which simultaneously softens a surface and shrinks it, even if it is highly irregular.
Only, so far, several boundary To this techniques, since in some situations the surface may stand out abruptly, or may be tuned to a point where the curvature “bursts” to infinity.
What mathematicians want to ensure, says, even after the formation of a singularity, they can continue to analyze the way the surface will continue to evolve.
To ensure that it is still possible to apply this technique, theconjecture of the “multiplicity-one”. It tells us that any singularities that are formed during the average curvature flow process should be relatively simple. The “bad” behavior should be limited to individual points.
In this field of geometry, “many of the results achieved so far depended on the conjecture of multiplicity-one to be true,” explains mathematician Richard Bamler. “Somehow, the main obstacle has always been the conjecture of a multiplicity-of a one.”
Now, Bamler and Bruce Kleiner have been able to prove in an ARXIV and published at the end of last year that The conjecture is true.
To exclude problematic situations, experts imagined an unusual way: what Kleiner called “a Maléfica chainid“It consists of two spheres, one inside the other, connected by a small cylinder, or neck, to form a single surface.
Through this method, mathematicians have excluded a “nightmare scenario”: the “separation function” changes over time, and mathematicians have proved that this nuna reaches zero.
“We now have a cfull transrupt of the flow of the average curvature of the surfaces In three -dimensional spaces, ”explained mathematician Otis Chodosh.
“Bamler and Kleiner gave us a huge advance in our understanding of the singularities in the heart of the middle curvature flow,” comments also mathematician Brian White. “It definitely opens the possibility of using it as a tool… to do all kinds of wonderful things.”
