Abstract
This paper introduces a notion of decompositions of integral varifolds into countably many integral varifolds, and the existence of such decomposition of integral varifolds whose first variation is representable by integration is established. However, the decompositions may fail to be unique. Furthermore, this result can be generalized by replacing the class of integral varifolds with some classes of rectifiable varifolds whose density is uniformly bounded from below; for these classes, we also prove a general version of the compactness theorem for integral varifolds.
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Acknowledgements
The author would like to thank his PhD advisor Prof. Ulrich Menne, Dr. Nicolau Sarquis Aiex, and Mr. Yu-Tong Liu for suggestions and consultations. The author would like to thank the referee for the careful reading of the manuscript and the suggestion to add Theorem 5.4. The author was supported by NTNU “Scholarship Pilot Program of the Ministry of Science and Technology to Subsidize Colleges and Universities in the Cultivation of Outstanding Doctoral Students”.
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The author has no relevant financial or non-financial interests to disclose. The author was supported by NTNU “Scholarship Pilot Program of the Ministry of Science and Technology to Subsidize Colleges and Universities in the Cultivation of Outstanding Doctoral Students”.
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Chou, HC. Integral decompositions of varifolds. Ann Glob Anal Geom 64, 3 (2023). https://doi.org/10.1007/s10455-023-09908-x
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DOI: https://doi.org/10.1007/s10455-023-09908-x