Analysis of boundary bubbles for almost minimal cylinders

作者：Rupflin Melanie^*; Schrecker Matthew R I

来源：Calculus of Variations and Partial Differential Equations, 2018, 57(5): 121.

DOI：10.1007/s00526-018-1397-8

We analyse the asymptotic behaviour of solutions of the Teichmuller harmonic map flow from cylinders, and more generally of 'almost minimal cylinders', in situations where the maps satisfy a Plateau-boundary condition for which the three-point condition degenerates. We prove that such a degenerating boundary condition forces the domain to stretch out as a boundary bubble forms. Our main result then establishes that for prescribed boundary curves that satisfy a separation condition, these boundary bubbles will not only be harmonic but will themselves be branched minimal immersions. Together with earlier work, this in particular completes the proof that the Teichmuller harmonic map flow changes every initial surface in spanning such boundary curves into a solution of the corresponding Douglas-Plateau problem.

• 出版日期2018-10