MathOverflow

Consider $M$ a manifold and $g_1, g_2$ two different Riemannian metrics. I want to know how the condition $|\nabla^{g_1,k}(g_1-g_2)|_{g_1}\leq C$ implies that the norms of $|\nabla^{g_1,i}u|_{T^{\otimes i}M, g_1}$ and $|\nabla^{g_2,i}u|_{T^{\otimes i...

I will call a two-player, symmetric, zero sum game a "tournament game" if both players have the same set of actions which correspond to the vertices of a tournament graph, and a player receives +1 payoff iff the edge joining the moves originates on their...

Let $K$ be a field, $A$ a semisimple $K$-algebra, $p$ its minimal primitive idempotent, $M=Ap$ a minimal left ideal, and $D=End_A(M)$ a K-division algebra. Assume a $K$-vector space $V$ to be isomorphic to $M^n$ and $\rho: A \to End_K(V)$ a representation...

Let $X$ be a measurable space and let $P$ be a probability distribution on $X \times \{\pm 1\}$. Let $F$ be a function class on $X$, i.e., a collection of (measurable) functions from $X$ to $\mathbb R$. Fix $\alpha \in \mathbb R$ and $\beta > 0$...