Regularity of harmonic maps from polyhedra to CAT(1) spaces
Regularity of harmonic maps from polyhedra to CAT(1) spaces
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DOI：
10.1007/s00526-017-1279-5
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发表时间：
2016-10
影响因子：
2.1
通讯作者：
Christine Breiner;A. Fraser;Lan-Hsuan Huang;Chikako Mese;Pam Sargent;Yingying Zhang
中科院分区：
文献类型：
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作者：
Christine Breiner;A. Fraser;Lan-Hsuan Huang;Chikako Mese;Pam Sargent;Yingying Zhang
我们确定了从n维黎曼多面体复合体x到CAT(1)空间的能量最小化映射的正则性结果。假设度量在x上是Lipschitz正则，我们证明了Hölder正则性，其中Hölder常数和指数依赖于映射的总能量和域上的度量。此外，在远离骨架的点，我们将正则性提高到局部利普希茨。最后，对于点与，我们证明了Hölder指数依赖于链接的几何和组合数据。
We determine regularity results for energy minimizing maps from ann-dimensional Riemannian polyhedral complexXinto a CAT(1) space. Provided that the metric onXis Lipschitz regular, we prove Hölder regularity with Hölder constant and exponent dependent on the total energy of the map and the metric on the domain. Moreover, at points away from the-skeleton, we improve the regularity to locally Lipschitz. Finally, for pointswith, we demonstrate that the Hölder exponent depends on geometric and combinatorial data of the link of.