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De Lellis's density conjecture for the Lavrentiev gap
For a homology class $[\Sigma]$ and coefficient ring $R$ , define the Lavrentiev-gap set by … Here $g$ ranges over the space of smooth Riemannian metrics. De Lellis's density conjec…
Conjectureopengeometric-measure-theory lavrentiev-phenomenon riemannian-geometryarXiv posted 2 days ago
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Large singular sets force the Lavrentiev phenomenon
Large-singular-set conjecture. If a minimizer has a large singular set, for example of Hausdorff dimension one, then a Lavrentiev gap must occur between the infimum over absolutely…
Conjectureopencalculus-of-variations lavrentiev-phenomenon singular-setsarXiv posted 2 days ago

De Lellis's density conjecture for the Lavrentiev gap