THE PLUMBING OF MINIMAL AREA SURFACES

[摘要] We study the metric of minimal area on a punctured Riemann surface under the condition that all nontrivial homotopy closed curves be longer than or equal to 2pi. By constructing deformations of admissible metrics we establish necessary conditions on minimal area metrics and a partial converse to Beurling's criterion for extremal metrics. We explicitly construct new minimal area metrics that do not arise from quadratic differentials. Under the physically motivated assumption of existence of the minimal area metrics, we show there exist neighborhoods of the punctures isometric to a flat semi-infinite cylinder of circumference 2pi, allowing the definition of canonical complex coordinates around the punctures. The plumbing of surfaces with minimal area metrics is shown to induce a metric of minimal area on the resulting surface. This implies that minimal area string diagrams define a consistent quantum closed string field theory.

[发布日期] 1994-12-01

[关键词] MINIMAL AREA RIEMANN SURFACES;QUANTUM STRING THEORY