Calculus of Variations and Geometric Measure Theory

D. Mucci

The relaxed p-energy of manifold constrained mappings

created by mucci on 30 Dec 2024

[BibTeX]

Accepted Paper

Inserted: 30 dec 2024
Last Updated: 30 dec 2024

Journal: Rendiconti del Circolo Matematico di Palermo
Year: 2024
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Abstract:

The $p$-energy of Sobolev mappings between Riemannian manifolds is studied, for each integer $p$ greater than two. We analyse the lower semicontinuous extension of the energy to currents. We then restrict to mappings with values into the $p$-sphere, by giving an explicit relaxed $p$-energy formula, whose proof depends on a strong density result. Finally, a related coarea formula is obtained.

Keywords: currents, coarea formula, Riemannian manifolds, Relaxed energy, Sobolev mappings


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