TY - JOUR
T1 - The dual Minkowski problem for negative indices
AU - Zhao, Yiming
N1 - Publisher Copyright:
© 2017, Springer-Verlag Berlin Heidelberg.
PY - 2017/4/1
Y1 - 2017/4/1
N2 - Recently, the duals of Federer’s curvature measures, called dual curvature measures, were discovered by Huang et al. (Acta Math 216:325–388, 2016). In the same paper, they posed the dual Minkowski problem, the characterization problem for dual curvature measures, and proved existence results when the index, q, is in (0, n). The dual Minkowski problem includes the Aleksandrov problem (q= 0 ) and the logarithmic Minkowski problem (q= n) as special cases. In the current work, a complete solution to the dual Minkowski problem whenever q< 0 , including both existence and uniqueness, is presented.
AB - Recently, the duals of Federer’s curvature measures, called dual curvature measures, were discovered by Huang et al. (Acta Math 216:325–388, 2016). In the same paper, they posed the dual Minkowski problem, the characterization problem for dual curvature measures, and proved existence results when the index, q, is in (0, n). The dual Minkowski problem includes the Aleksandrov problem (q= 0 ) and the logarithmic Minkowski problem (q= n) as special cases. In the current work, a complete solution to the dual Minkowski problem whenever q< 0 , including both existence and uniqueness, is presented.
KW - 52A40
UR - http://www.scopus.com/inward/record.url?scp=85011912114&partnerID=8YFLogxK
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U2 - 10.1007/s00526-017-1124-x
DO - 10.1007/s00526-017-1124-x
M3 - Article
AN - SCOPUS:85011912114
SN - 0944-2669
VL - 56
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 2
M1 - 18
ER -