All Questions

Let $U_1\subset \mathbb R^3$ be a simply connected bounded open set with a smooth boundary and let $U_2$ be a neighborhood of $U_1$. Does there exist a real-analytic diffeomorphism $\psi: U_2 \to W_2$ ...

Let $M \subset \mathbb{R}^p$ be a Riemannian submanifold. In what follows, when we talk about a Lipschitz function $f$ on $M$, namely $f: M \to \mathbb{R}$, we will assume there is a $L > 0$ so ...

Let $I = [t_{0}, t_{1}]$ be a closed interval with $t_{0} < t_{1}$ and let $M$ be a compact real analytic $n$-dimensional manifold without boundary. Furthermore, let $f:I \times M \rightarrow \...