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Dynamical Equations For The Period Vectors In A Periodic System Under Constant External Stress
The purpose of this paper is to derive the dynamical equations for the period
vectors of a periodic system under constant external stress. The explicit
starting point is Newton's second law applied to halves of the system. Later
statistics over indistinguishable translated states and forces associated with
transport of momentum are applied to the resulting dynamical equations. In the
final expressions, the period vectors are driven by the imbalance between
internal and external stresses. The internal stress is shown to have both full
interaction and kinetic-energy terms.Comment: 10 pages, 2 figures include
On the volume growth of K\"ahler manifolds with nonnegative bisectional curvature
Let be a complete K\"ahler manifold with nonnegative bisectional
curvature. Suppose the universal cover does not split and admits a
nonconstant holomorphic function with polynomial growth, we prove must be
of maximal volume growth. This confirms a conjecture of Ni. There are two
essential ingredients in the proof: The Cheeger-Colding theory on
Gromov-Hausdorff convergence of manifolds; the three circle theorem for
holomorphic functions.Comment: 12 page
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