Harmonic maps from degenerating Riemann surfaces

By Miaomiao Zhu. 2008

66 citations recorded by the source corpus.

We study harmonic maps from degenerating Riemann surfaces with uniformly bounded energy and show the so-called generalized energy identity. We find conditions that are both necessary and sufficient for the compactness in W1,2 and C0 modulo bubbles of sequences of such maps.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2acefaa39899bd186a0f83d57a8931ac33c1da68

How researchers see this paper

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In Applied Mathematics

1. T. Rivière
2. Yann Bernard
3. Yuxiang Li
4. Ernst Kuwert
5. Armin Schikorra
6. Michael Struwe
7. T. Lamm
8. Y. Yang

In Geometry and Topology

1. T. Rivière
2. Yuxiang Li
3. Ernst Kuwert
4. Yann Bernard
5. Klaus Deckelnick
6. Gerhard Dziuk

Citations in the corpus

• Energy quantization for Willmore surfaces and applications (2011, background): “ann surface into a manifold are known in general not to satisfy the energy quantization property in the thin collar regions (cf. example constructed in [Pa], and the careful systematic study given in [Zhu]). Questions 4Indeed, in a conformal parametrization ~ξ, the Willmore functional may be recast ”
• $W^{2,2}$-conformal immersions of a closed Riemann surface into $\R^n$ (2010, methodology): “For this we refer to Section 4 in [22].”