Yet another normalisation proof for Martin-Lof's logical framework--Terms with correct arities are strongly normalising

In this paper, we prove the strong normalisation for Martin-L\"{o}f's Logical Framework, and suggest that {}``correct arity'', a condition weaker than well-typedness, will also guarantee the strong normalisation.Comment: 19 page

On conformal surfaces of annulus type

Let $a>b>0$ and $f$ be a conformal map from $B_a\setminus B_b\subseteq R^2$ into $\R^n$, with $|\nabla f|^2=2e^{2u}$. Then $(e_1, e_2)$ with $e_1=e^{-u}\frac{\partial f}{\partial r},$ and $e_2=r^{-1}e^{-u}\frac{\partial f}{\partial\theta}$ is a moving frame on $f(B_a\setminus B_b)$. It satisfies the following equation $$d\star=0,$$ where $\star$ is the Hodge star operator on $R^2$ with respect to the standard metric. We will study the Dirichret energy of this frame and give some applications.Comment: Some typos have been polished and I find that the best constant for L^infinity norm in Wente inequality has been established by Topping in a paper dated to 199