Constructing Universal Abelian Covers of Graph Manifolds

To a rational homology sphere graph manifold one can associate a weighted tree invariant called splice diagram. It was shown earlier that the splice diagram determines the universal abelian cover of the manifold. We will in this article turn the proof of this in to an algorithm to explicitly construct the universal abelian cover from the splice diagram.Comment: 12 page

Determining When The Universal Abelian Cover of a Graph Manifold is a Rationla Homology Sphere

It was shown in my earlier article that the splice diagram of a rational homology sphere graph manifold determines the manifolds universal abelian cover. In this article we use the proof of this to give a condition on the splice diagram to determine when the universal abelian cover itself is a rational homology sphere.Comment: 13 page

Minimal surface singularities are Lipschitz normally embedded

Any germ of a complex analytic space is equipped with two natural metrics: the {\it outer metric} induced by the hermitian metric of the ambient space and the {\it inner metric}, which is the associated riemannian metric on the germ. We show that minimal surface singularities are Lipschitz normally embedded (LNE), i.e., the identity map is a bilipschitz homeomorphism between outer and inner metrics, and that they are the only rational surface singularities with this property.Comment: This paper is a major revision of the 2015 version. It now builds on the paper arXiv:1806.11240 by the same authors which gives a general characterization of Lipschitz normally embedded surface singularitie

A characterization of Lipschitz normally embedded surface singularities

Any germ of a complex analytic space is equipped with two natural metrics: the outer metric induced by the hermitian metric of the ambient space and the inner metric, which is the associated riemannian metric on the germ. These two metrics are in general nonequivalent up to bilipschitz homeomorphism. We give a necessary and sufficient condition for a normal surface singularity to be Lipschitz normally embedded (LNE), i.e., to have bilipschitz equivalent outer and inner metrics. In a partner paper [15] we apply it to prove that rational surface singularities are LNE if and only if they are minimal.Comment: 30 page

Varmepumper og Lavtemperatur-fjernvarme - Rapportering fra to workshops

Denne rapport udgør et delbidrag af rapporteringen fra projektet ” Effektiv fjernvarme i fremtidens energisystem”, som under Energistyrelsens Energiforskningsprogram (EFP) udføres af et konsortium af EA-energianalyse, Systemanalyseafdelingen på Risø DTU, RAM-løse edb samt Fjernvarmens visionsudvalg nedsat under Dansk Fjernvarmeforening.Formålet med projektet er at belyse, hvordan fjernvarmens rolle i energiforsyningen kan udvikles på langt sigt gennem effektiv drift, anvendelse af ny teknologi samt dynamisk samspil med elmarkedet. En fremtidig udvikling mod et bæredygtigt energisystem vil kræve betydelige energibesparelser, herunder i rumopvarmningen. Dette vil alt andet lige mange steder føre til, at grundlaget for fjernvarmen vil ændre sig. Det er således centralt i projektet, at opstille en række scenarier for fjernvarmens fremtidige rolle i energisystemet, herunder at belyse hvad reducerede varmetab i fjernvarmenet og dynamisk anvendelse af kendte og nye energiteknologier kan betyde. Disse teknologier omfatter bl.a. varmepumper, geotermi, fjernkøling og varmelagring. Endvidere er formålet at belyse hvordan samspillet mellem elmarkedet og fjernvarmen kan effektiviseres, samt at pege på hvilke rammebetingelser der især er kritiske for fjernvarmens fortsatte udvikling og effektivisering.Som et led i analyserne i projektet er der afholdt to workshops om henholdsvis anvendelsen af varmepumper og lavtemperatur-fjernvarmenet. Denne rapport er en dokumentation af de to workshops, idet den indeholder program, deltagerliste, præsentationer og korte resumeer. I begge workshops deltog eksterne indledere parallelt med projektgruppens egne deltagere. Vi takker deltagerne for præsentationer og engageret deltagelse i diskussionerne