arXiv research

CR Paneitz operator on non-embeddable tori has infinitely many negative eigenvalues

Study on CR Paneitz operator on non-embeddable CR manifolds.

It is proved that the suspension of a closed n-dimensional manifold M, $n\ge1$, does not embed in a product of n+1 curves. In fact, the ultimate result will be proved in a much more general setting. This is a far-reaching generalization the Borsuk theorem on non-embeddability of the (n+1)-dimensional sphere in a produc…

New proof shows non-embeddable polyhedra and conditions for embedding products.

We give local criteria for smooth non-embeddablity of Levi-flat manifolds. For this purpose, we pose an analogue of Ueda theory on the neighborhood structure of hypersurfaces in complex manifolds with topologically trivial normal bundles.

We define a way of approximating actions on measure spaces using finite graphs; we then show that in quite general settings these graphs form a family of expanders if and only if the action is expanding in measure. This provides a somewhat unified approach to construct expanders. We also show that the graphs we obtain …

For an evolution of metrics $(M,g_{t})$ there is a t-smooth family of embeddings $e_{t}:M\to\mathbb{R}^{N}$ inducing $g_{t}$, but in general there is no family of embeddings extending a given initial embedding $e_{0}$. We give an example of this phenomenon when $g_{t}$ is the evolution of $g_{0}$ under the Ricci flow. …

The abstract applies waist inequality to dynamical systems and entropy.

A simplified proof for embedding higher-dimensional complexes into manifolds.

We define an ADM-like mass, called p-mass, for an asymptotically flat pseudohermitian manifold. The p-mass for the blow-up of a compact pseudohermitian manifold (with no boundary) is identified with the first nontrivial coefficient in the expansion of the Green function for the CR Laplacian. We deduce an integral formu…

Study examines Wang-Yau quasi-local energy in strong fields near apparent horizons.

We review a cochain-free treatment of the classical van Kampen obstruction θto embeddability of an n-polyhedron into R^{2n} and consider several analogues and generalizations of θ, including an extraordinary lift of θwhich in the manifold case has been studied by J.-P. Dax. The following results are obtained. - The mod…

Classifies critical complexes for embedding in 3-sphere.