Harnack-type mass bounds and bernstein theorems for area-minimizing flat chains modulo v.
- 1 January 1986
- journal article
- research article
- Published by Taylor & Francis in Communications in Partial Differential Equations
- Vol. 11 (12) , 1257-1283
- https://doi.org/10.1080/03605308608820464
Abstract
For an area-minimizing flat chain modulo v with no boundary inside the unit ball, an absolute upper bound is given for the amount of area inside a shrunken ball. Such Harnack-type estimates lead to generalizations of area inside a shrunken ball. Such Harnack-type estimates lead to generalizations of Bernstein's Theorem. For example, for n⪇5, a 2-dimensional, area-minimizing locally flat chain modulo 2 without boundary in IRn which has at least 1 singularity must consist of 2 orthogonal planes.Keywords
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