arXiv research

Extends Polydisk Theorem to Cartan-Hartogs domains.

Extends polydisk theorem to Hartogs domains over symmetric domains.

Studies acceptable bundles on a partially punctured polydisk.

New symplectic embedding obstructions found for polydisks into half-integer ellipsoids.

We study the family of holomorphic maps from the polydisk to the disk which restrict to the identity on the diagonal. In particular, we analyze the asymptotics of the orbit of such a map under the conjugation action of a unipotent subgroup of $\text{PSL}_2(\mathbb{R})$. We discuss an application our results to the stud…

The paper proves properties of complex Finsler metrics on specific domains.

We completely solve the symplectic packing problem with equally sized balls for any rational, ruled, symplectic 4-manifolds. We give explicit formulae for the packing numbers, the generalized Gromov widths, the stability numbers, and the corresponding obstructing exceptional classes. As a corollary, we give explicit va…

Let $X$ be a compact complex manifold and $E$ be a holomorphic vector bundle on $X$. Given a deformation $(\mathcal{X},\mathcal{E})$ of the pair $(X,E)$ over a small polydisk $B$ centered at the origin, we study the jumping phenomenon of the cohomology groups $\dim_{\mathbb{C}}H^q(\mathcal{X}_t,\mathcal{E}_t)$ near $t …

Let $(M, g)$ be a real analytic Kaehler manifold. We say that a smooth map $E_p:W\to M$ from a neighborhood $W$ of the origin of $T_pM$ into $M$ is a {\em diastatic exponential} at $p$ if it satisfies $$(d \E_p)_0=\id_{T_pM},$$ $$D_p(\E_p (v))=g_p(v, v), \forall v\in W,$$ where $D_p$ is Calabi's diastasis function at $…

Let M be a closed symplectic manifold of volume V. We say that M admits an unobstructed symplectic packing by balls if any collection of symplectic balls (of possibly different radii) of total volume less than V admits a symplectic embedding to M. In 1994 McDuff and Polterovich proved that symplectic packings of Kahler…

Symplectic embeddings of balls into specific manifolds are studied, with restrictions and obstructions identified.