arXiv subjects
Publications and source records attributed to Peter Polyakov.
In this paper, we have proposed a two phase procedure (combining discrete graphs and wavelets) for constructing a true epidemic growth. In the first phase graph theory based approach was developed to update partial data available and in the second phase we used this partial data to generate a plausible complete data through wavelets. This procedure although novel and implementable, still leave some questions unanswered.
Let ${\bold M}_0$ be a compact, regular q-pseudoconcave compact CR submanifold of a complex manifold ${\bold G}$ and ${\cal B}$ - a holomorphic vector bundle on ${\bold G}$ such that $\dim H^r({\bold M}_0, {\cal B}\big|_{\bold M})=0$ for some fixed $r<q$. We prove a global homotopy formula with $C^k$ estimates for $r$-cohomology of ${\cal B}$ on arbitrary CR submanifold ${\bold M}$ close enough to ${\bold M}_0$.
We prove that for an induced CR structure on a compact, generic, regular 3-pseudoconcave CR submanifold ${\bold M}\subset{\bold G}$, of a complex manifold ${\bold G}$, satisfying condition $\dim H^1({\bold M}, T^{\prime}({\bold G})|_{\bold M})=0$ all the close CR structures are induced by close embeddings.
We construct integral homotopy operators on a regular CR manifold and prove sharp estimates for these operators in a special Lipschitz scale.