The Ricci Flow《还是陶哲轩的RICCI FLOW 通俗点》

还是陶哲轩的RICCI FLOW 科普点。

“For instance in one atlas the city of Los

Angeles might be on the boundary of one of the charts whereas in another atlas it

might be in the interior of any chart that it appears in. However there are many

facts one can deduce from an atlas which do not depend on the choice of atlas;

for instance using any accurate atlas of the Earth one can see that one cannot

travel from Los Angeles to Sydney without crossing at least one ocean. If a fact

regarding a surface does not depend on which atlas one uses we say that it is

intrinsic or coordinate-independent. It will turn out that Ricci flow is an intrinsic

flow on surfaces; it can be defined without any knowledge of charts or of an extrinsic

ambient space.”....

我喜欢这种交谈式的讲授