# A Campanato Regularity Theory for Multi-Valued Functions with Applications to Minimal Surface Regularity Theory

@inproceedings{Minter2021ACR, title={A Campanato Regularity Theory for Multi-Valued Functions with Applications to Minimal Surface Regularity Theory}, author={Paul Minter}, year={2021} }

. The regularity theory of the Campanato space L ( q,λ ) k (Ω) has found many applications within the regularity theory of solutions to various geometric variational problems. Here we extend this theory from single-valued functions to multi-valued functions, adapting for the most part Campanato’s original ideas ([Cam64]). We also give an application of this theory within the regularity theory of stationary integral varifolds. More precisely, we prove a regularity theorem for certain blow-up…

## One Citation

### The Structure of Stable Codimension One Integral Varifolds near Classical Cones of Density $Q+1/2$

- Mathematics
- 2021

. For each positive integer Q ∈ Z ≥ 2 , we prove a multi-valued C 1 ,α regularity theorem for varifolds in the class S Q , i.e., stable codimension one stationary integral n -varifolds which have no…

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