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Volume-preserving flow by powers of the mth mean curvature:

Cabezas-Rivas, Esther ; Sinestrari, Carlo
Calculus of Variations and Partial Differential Equations.  38 (2009)  3-4 - p. 441-469 , 2009
Link: https://doi.org/10.1007/s00526-009-0294-6