abstract: We prove existence, uniqueness and regularity of solutions to the Einstein vacuum equations taking form $$ {}^{(4)}g = -dt^2 + \sum_{i,j=1}^3 a_{ij}t^{2 p_{\max\{i,j\}}}\,{\rm d} x^i\,{\rm x^j on $(0,T]_t\times\Bbb{T}^3_x$, where $a_{ij}(t,x)$ $p_i(x)$ are regular functions without symmetry or analyticity assumptions. These metrics singular asymptotically Kasner-like as $t\to 0^+$. ex...

We study a class of asymptotically cylindrical Ricci-flat Kähler metrics arising on quasiprojective manifolds. Using the Calabi–Yau geometry and analysis and the Kodaira–Kuranishi–Spencer theory and building up on results of N.Koiso, we show that under rather general hypotheses any local asymptotically cylindrical Ricci-flat deformations of such metrics are again Kähler, possibly with respect t...

This paper discusses the asymptotic efficiency of estimators for optimal portfolios when returns are vector-valued non-Gaussian stationary processes. We give the asymptotic distribution of portfolio estimators ĝ for non-Gaussian dependent return processes. Next we address the problem of asymptotic efficiency for the class of estimators ĝ. First, it is shown that there are some cases when the as...