10 problems

Let $H$ be a manifold with corners and let $D_H$ be a cusp pseudodifferential operator of order $1$ that is of Dirac type near the boundary, as in the referenced theorem and remark…

Positive-injectivity-radius conjecture. All Riemannian manifolds with Lie structures at infinity have positive injectivity radius:

Manifold-with-corners conjecture. There is an open neighborhood $U$ of $\sigma$ such that this map is a homeomorphism from $U$ onto an open subset of $\mathcal{A}^{\mathbb{R}}_n$.

Manifold-with-corners conjecture. The map $\ell_{(-)}(E_1,\ldots,E_n)$ induces a homeomorphism from an open neighborhood of $\sigma$ onto an open subset of…

The paper considers controllability results for diffeomorphism groups of simple polytopes, including generation of the identity component by exponentials of suitable vector fields…

A generalized product consists of manifolds with corners $M[k]$ associated contravariantly to finite sets, with the structure maps satisfying the generalized-product conditions. A…

Let $M$ be a manifold with corners and let $\mathcal S$ be a clean semilattice of closed p-submanifolds of $M$. The iterated blow-up $[M:\mathcal S]$ is mapped by…

Let $M$ be a manifold with corners and let $P,Q$ be suitable closed p-submanifolds of $M$. The map $\mathcal B_{M,Q,P}$ has image in $[M:P]\times[M:Q]$. The b- and wib-submanifold…

Let $G$ be a real reductive Lie group with compact center, and let an hd-compactification of $G$ be a compact manifold with corners $\overline{G}$ containing $G$ as its interior an…

Let $H$ be a compatible Laplacian on a manifold with corners of codimension $2$, and call an eigenvalue embedded when it lies in the continuous spectrum of $H$. Generic absence con…