Osmo Pekonen

Quasidisks and string theory

Abstract A heuristic model of non-perturbative bosonic string theory on the Bers universal Teichmuller space of normalized quasidisks is discussed. It is suggested that the infinite-dimensional analogue of the Polyakov energy might be the quasidisk area.

On the variational characterization on conformally flat 3-manifolds

Abstract We review the characterization of conformally flat structures on a compact 3-manifold as the critical points of the Chern-Simons functional on Conformal Superspace. As a matter of fact, the formulas for the first and second variation of the Chern-Simons functional can essentially be found in the existing literature but we state the results more explicitly here and add some new remarks. In particular, pursuing our previous study [17], we want to keep track of the special properties of the DeWitt metric.

The Einstein field equation in a multidimensional universe

String theory [4] predicts that the universe has 10 or 26 dimensions. A salient problem is how the Einstein field equation should be written in terms of these revivified Kaluza-Klein cosmologies. The answer is by now well-known, yet nobody seems to have rewritten the seminal computation in [6] where an unnecessarily involved Euler-Lagrange variational method is employed and, curiously enough, no allusion to the Gauss-Bonnet-Chern theorem is made. We provide a more straightforward argument, which has been inspired by Hilberts original derivation of the Einstein field equation [5].