AbstractWe discuss the regularity properties of weak solutions of certain degenerate elliptic systems arising from problems in geometry. For example we proveC1‐regularity of conformalm‐harmonic maps from them‐ball intom‐dimensional oriented submanifolds ofRm+1as well as a regularity theorem for weakH‐surfaces inRm+1. Our arguments make strong use of a version of the isoperimetric i
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