2 problems

Let $V$ be decomposed into a resolved effective potential $U_k=V_0+\sum_{j=1}^{k}V_{j,\varepsilon_j}$ and under-resolved microscopic components…

Let $M$ be a compact $n$-dimensional manifold, let $g=e^{2\varphi}g_0$ range over a conformal class of metrics, let $v$ be a positive warp factor, and let $F^{(p)}$ be the field st…