Is there a L-Lipschitz homeomorphism of the Elipse $x^2/4+y^2=1$ onto the unit circle $x^2+y^2=1$ such that $L<1$?

The same colleague as in http://mathoverflow.net/questions/130489/another-colored-balls-puzzle asked me the following variant which she called "part II". Imagine you have $n$ ball …

I asked this on mathStackexchange but might be a bit too localized for it. I am reading Beauville's chapter IX on Elliptic surfaces. Let $S$ be a minimal elliptic surface with $\ …

The concept of relation in the history of mathematics, either consciously or not, has always been important: think of order relations or equivalence relations. Why was there the n …

The action of a group $G$ on a topological space $X$ can be viewed as a functor $F: G \to \mathcal{Top}$ with $F(*)=X$. (Here I'm viewing a group as a category with one object, $ * …

I am looking for the relations and analogies between the Perelman's entropy functional,$\mathcal{W}(g,f,\tau)=\int_M [\tau(|\nabla f|^2+R)+f-n] (4\pi\tau)^{-\frac{n}{2}}e^{-f}dV$, …

Let $\alpha$ be any positive irrational and $\beta$ be any positive real. We have the following results. H. Weyl (1909): The fractional part of the sequence $\alpha n$ is equidist …

In 1968, Arnol'd proved that the integral cohomology of the pure braid group $P_n$ is isomorphic to the exterior algebra generated by the collection of degree-one classes $\omega_{ …

This question deals with the gamma factor of a function of the Selberg class. Writing the functional equation of such a function $F$ as $\Phi(s)=\overline{\Phi(\overline{1-s})}$ wi …

A real closed field can be ordered in one and only one way, and is therefore provided with a unique order topology. Given any infinite cardinal number k, does there always exist a …

I am usually confused by questions of the type "could such and such a problem be undecidable", because as far as I know there are two distinct possible meanings of "undecidable". …

I know how to pack $5$ unit squares in a square of side length $2+\frac{\sqrt{2}}{2}$. Is there an $\varepsilon>0$ such that there exists a packing of $9$ unit cubes in a cube of …

I am interested in the zero-set of a homogeneous function $f(x_1, \cdots, x_n)$, where $f$ is not necessarily a polynomial. In particular, I would like to know if there are any gen …

I have started reading "Introduction to differentiable manifolds" by Serge Lang. In this book, Lang takes a different approach, by immediately introducing manifolds on arbitrary Ba …

It is known that if a variety is unirational then it is rationally connected. However, there are no known examples of rationally connected varieties which are not unirational. In …