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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.17226 |
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Table of Contents:
- We show the existence of some special coordinate systems for expressing maps with branch points. These coordinates allow obtaining an explicit representation formula of branch immersions and understanding the regularity of some fundamental elements in the theory of R. D. Gulliver, R. Osserman and H. L. Royden. For conformal maps, we prove that these coordinates exist with certain regularity if and only if the mean curvature vector extends and is in a particular Hölder space. In the general case, we characterize this type of coordinate system. Also, using these coordinates, we study the regularity and behavior of curvatures near branch points.