A corrected proof of the graphical representation of a class of curvature varifolds by C 1,α multiple valued functions
Year: 2026
Type: article
Abstract: We provide a counter-example to Hutchinson’s original proof of C 1 , α {C^{1,\alpha}} representation of curvature m -varifolds with L q {L^{q}} -integrable second fundamental form and q > m {q>m} in [J. E. Hutchinson, C 1 , α {C^{1,\alpha}} multiple function regularity and tangent cone behaviour for varifolds with second fundamental form in L p {L^{p}} , Geometric Measure Theory and the Calculus of Variations (Arcata 1984), Proc. Sympos. Pure Math. 44, American Mathematical Society, Providence 1986, 281–306]. We also provide an alternative proof of the same result and introduce a method of decomposing varifolds into nested components preserving weakly differentiability of a given function. Furthermore, we prove the structure theorem for curvature varifolds with null second fundamental form which is widely used in the literature.
Author: Nicolau S. Aiex
Institution: National Taiwan Normal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,712
Award: G8297519375
OpenAlex ID: W7155617657