Harmonic Maps with Free Boundary from Degenerating Bordered Riemann Surfaces

作者：Liu, Lei; Song, Chong; Zhu, Miaomiao^*

来源：JOURNAL OF GEOMETRIC ANALYSIS, 2022, 32(2): 49.

DOI：10.1007/s12220-021-00834-7

• Harmonic map
• Degenerating bordered Riemann surface
• Free boundary
• Blow-up

We study the blow-up analysis and qualitative behavior for a sequence of harmonic maps with free boundary from degenerating bordered Riemann surfaces with uniformly bounded energy. With the help of Pohozaev type constants associated to harmonic maps defined on degenerating collars, including vertical boundary collars and horizontal boundary collars, we establish a generalized energy identity.

• 单位
  厦门大学; 上海交通大学