24
votes
0answers
505 views
+250

3-colorings of the unit distance graph of $\Bbb R^3$

Let $\Gamma$ be the unit distance graph of $\Bbb R^3$: points $(x,y)$ form an edge if $|x,y|=1$. Let $(A,B,C,D)$ be a unit side rhombus in the plane, with a transcendental diagonal, e.g. $A = ...
3
votes
0answers
92 views
+50

Lipschitz continuity of a composition operator

Let $M$ be a compact Riemannian submanifold of $\mathbb{R}^K$, $U\subset \mathbb{R}^K$ an open neighboorhood of $M$ such that the shortest point Projection $P_M\colon U\rightarrow M$ is well-defined ...
4
votes
1answer
175 views
+50

Will (general points + small number of arbitrary points) impose independent condtions on plane curves?

It is well known that imposing vanishing at general points of $\mathbb P^2$ gives independent conditions on curves of degree $d$. Also, it is known that a small number ($\le d+1$) points always impose ...
0
votes
0answers
93 views
+50

About expectation norms on graphs

Let $S \subseteq V$ of a $d-$regular graph $G$ such that $\mu = \frac{\vert S \vert }{\vert V \vert } $. Let $A$ be the adjacency matrix of the graph. Then define the quantity $\phi(S)= ...
0
votes
0answers
103 views
+50

Local coordinates on (infinite dimensional) Lie groups, factorization of Rieman zeta functions

Given a (finite dimensional) Lie group $G$ (real $k=\mathbb{R}$ or complex $k=\mathbb{C}$) and its Lie algebra $\mathfrak{g}$, one can prove (a basis $B=(b_i)_{1\leq i\leq n}$ of $\mathfrak{g}$ being ...