Alessandro Carlotto, Chao Li
We prove a novel desingularization theorem, that allows to smoothly attach two given manifolds with corners by suitably gluing a pair of isometric faces, with control on both the scalar curvature of the resulting space and the mean curvature of its boundary.
This paper contains 7 sections, 12 theorems, 72 equations.
Lemma 2.1
Let us consider on the product manifold $M=X\times J$ a smooth metric of the form where $u\in C^{\infty}(M)$ and the map $J\ni t \mapsto h_t(x)\in \mathscr R(X)$ is also smooth. Then the following formulae hold: (Note that, for the first two equations we have considered $X\times\left\{t\right\}$ as boundary of $X\times [0,t]$, i. e. we worked with respect to the normal $\partial_t$).
