TY - JOUR
T1 - Regularity of shadows and the geometry of the singular set associated to a monge-Ampere equation
AU - Indrei, E.
AU - Nurbekyan, Levon
N1 - KAUST Repository Item: Exported on 2020-10-04
PY - 2016/11/3
Y1 - 2016/11/3
N2 - Illuminating the surface of a convex body with parallel beams of light in a given direction generates a shadow region. We prove sharp regularity results for the boundary of this shadow in every direction of illumination. Moreover, techniques are developed for investigating the regularity of the region generated by orthogonally projecting a convex domain onto another. As an application we study the geometry and Hausdorff dimension of the singular set corresponding to a Monge-Ampere equation.
AB - Illuminating the surface of a convex body with parallel beams of light in a given direction generates a shadow region. We prove sharp regularity results for the boundary of this shadow in every direction of illumination. Moreover, techniques are developed for investigating the regularity of the region generated by orthogonally projecting a convex domain onto another. As an application we study the geometry and Hausdorff dimension of the singular set corresponding to a Monge-Ampere equation.
UR - http://hdl.handle.net/10754/665404
UR - http://www.intlpress.com/site/pub/pages/journals/items/cag/content/vols/0024/0004/a005/
UR - http://www.scopus.com/inward/record.url?scp=84994777515&partnerID=8YFLogxK
U2 - 10.4310/CAG.2016.v24.n4.a5
DO - 10.4310/CAG.2016.v24.n4.a5
M3 - Article
SN - 1944-9992
VL - 24
SP - 793
EP - 820
JO - Communications in Analysis and Geometry
JF - Communications in Analysis and Geometry
IS - 4
ER -