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Unique Continuation for Area Minimizing Currents
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DOI：10.1007/s00205-026-02190-8.png)
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Abstract
En 中文
The main goal of this work is to prove an instance of the unique continuation principle for area minimizing integral currents. More precisely, we consider an m-dimensional area minimizing integral current and an m-dimensional minimal surface, both contained in $${\mathbb {R}}^{n+m}$$ with $$n\ge 1$$ . We show that if, in an integral sense, the current has an infinite order of contact with the minimal surface at a point, then the current and the minimal surface coincide in a neighbourhood of that point.
Keywords:
unique continuation
area minimizing currents
integral currents
minimal surfaces
geometric measure theory
Journal
IF:
2.4
Papers:
147
Citations:
1.2W