User kassandra - MathOverflow

Reference needed: Donsker's Invariance Principle for Riemannian Manifolds

2013-04-03T11:03:00Z

After an extensive unsuccessful search: I need a reference (preferably a book) for the Donsker's invariance principle for Riemannian manifolds. Thanks.

the left hand side of the Ricci flow equation at the initial value

2012-05-08T14:29:17Z

I just started to learn about the Ricci flow and try to understand the Ricci flow evolution equation. It states that a one-parameter family $g_t$, $t\in[0,T)$ of Riemannian metrics on a smooth closed manifold $M$ is a solution of the equation $$ \frac{\partial g_t}{\partial t}=-2 Ric_{g_t}. $$ But, in order to be able to write down the expression $$ \frac{\partial g_t}{\partial t} $$ I need a little bit more than the fact that $g_t$ is a one-parameter family of Riemannian metrics.

There are several ways to understand this expression, which probably are equivalent to each other. I think the most naive idea is to consider $g_t$ as a smooth curve in the infinite-dimensional vector space of all Riemannian metrics on $M$ and $\frac{\partial g_t}{\partial t}$ as tangent vectors to this curve.

Now, my question is: How do I have to understand the left hand side of the Ricci flow equation at the initial value $t=0$?

Does one consider $g_t$ as a smooth family at the open interval $(0,T)$ and requires continuity at the point $t=0$ or has one to deal with differentiability from the right?

Thank you very much!

Do you use the Mathematics Subject Classification (MSC) when searching for literature?

2012-05-07T14:21:23Z

I suppose most of you are familiar with the Mathematics Subject Classification (MSC). Particularly, when submitting an article for publication one has to choose appropriate classification codes.

But I am wondering if it does play a significant role in searching for literature on a specific subject, e.g. through MathSciNet or ZBMATH. Or do you prefer searching by subject terms?

Thank you very much!

Answer by kassandra for Sources for Bibtex entries

2012-05-07T13:07:00Z

I also use JabRef. In addition, there is an easy to use JabRef plugin for the Union Catalogue (GVK) of several German federal states participating in the so-called Common Library Network (GBV).

For JabRef see http://jabref.sourceforge.net/.

For downloading the JabRef-GBV-plugin see http://jabref.tempelb.de/.

Comment by kassandra

2013-04-03T18:49:43Z

@Carlo So far it looks very promising - and provides pretty much interesting reading material ... Thanks a lot! @Stephan Thank you very much for your helping hand.

Comment by kassandra

2012-05-14T08:14:01Z

Oh, Gerhard, you interestingly mentioned the term "thesaurus". Many subjects do come up with sophisticated thesauri, but due to my knowledge there is no community established thesaurus (in its proper meaning) in mathematics.

Comment by kassandra

2012-05-14T08:13:05Z

Tom wrote "Maybe there are other uses." Neil, here you brought a completely new aspect to the discussion: a use of the MSC in a certain project context. Does somebody know further projects involving the MSC or making use of it?

Comment by kassandra

2012-05-14T08:12:13Z

Joe, your answer confirms my impression that the idea of keeping up-to-date in a field that is outlined by a classification code is definitely worthwhile.

Comment by kassandra

2012-05-14T08:11:27Z

Neil, you wrote "This is the only use ..." but keeping up-to-date in a somewhat broader sense and not restricted to one's own specific research field seems to be more than most of us do today.

Comment by kassandra

2012-05-14T08:10:42Z

Tom, this is indeed a comprehensible argument, which is convincingly illustrated by a "tasty" example, but Yemon's comment beautifully shows that there is some evidence of the MSC in the case that one cannot use a known term search.

Comment by kassandra

2012-05-14T08:09:39Z

Henry, thank you very much for your response. I think the best that can happen to a question is that it sets off reflecting on something and gives way to a try. Obviously, there is a lot of agreement with your answer.

Comment by kassandra

2012-05-11T15:05:39Z

I just realized that my question is reopened. Thanks. I am looking forward to seeing your opinions.

Comment by kassandra

2012-05-08T20:01:25Z

Otis, thanks particularly for your valuable references to the literature.

Comment by kassandra

2012-05-08T19:49:53Z

I made it "community wiki". Anton, thank you for your advice.

Comment by kassandra

2012-05-08T18:30:47Z

Misha, that argument sounds plausible to me. Thank you very much!

Comment by kassandra

2012-05-08T12:11:20Z

Honestly, I only wanted to get an impression on the actual use of MSC. I am not in the mood to hold a meta discussion on whether or not to reopen my question.