In this note we consider an example to test three lower bounds presented in Diaconis– Stroock [4] (one by Diaconis and Stroock (DS), another by Sinclair (S) [9], and the third by Jerrum–Sinclair (JS)… (More)

A special case of Wirtinger's theorem asserts that a complex curve (two-dimensional) holomorphically embedded in a Kaehler manifold is a minimal surface. The converse is not necessarily true. Guided… (More)

Our “jungle gyms” are 2–dimensional differentiable manifolds M , with preferred Riemannian metrics, associated to graphs. Our interest is in proving that the validity of the Neumann–Cheeger… (More)

The inequality (1) is usually referred to as λ–transience of M. See [5]; also see [3]. We add that in [3] it is shown that, in general, eλtp always has a limit when t ↑ +∞, which either is… (More)