On the _{}-Minkowski problem

By Erwin Lutwak, Deane Yang, Gaoyong Zhang. 2003

168 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/9619f6b2e25eccdc8a4efe8f7c65c66fb9df195b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Yiming Zhao
2. Deping Ye
3. Gaoyong Zhang
4. Deane Yang
5. Erwin Lutwak
6. Christoph Haberl
7. Van Hoang Nguyen
8. Monika Ludwig

In Computer Vision and Pattern Recognition

1. Van Hoang Nguyen
2. Christos Saroglou
3. Christoph Haberl
4. Yiming Zhao
5. Gaoyong Zhang
6. Deane Yang
7. Erwin Lutwak
8. Deping Ye

In Geometry and Topology

1. Yiming Zhao
2. Deping Ye
3. Deane Yang
4. Gaoyong Zhang
5. Christoph Haberl
6. Erwin Lutwak
7. Christos Saroglou
8. Van Hoang Nguyen

Citations in the corpus

• The logarithmic Minkowski problem (2012, unknown): “In [45], it was shown that, for p 6= n, the Lp-Minkowski problem has an equivalent volume-normalized formulation, and (using a slightly modified approach) a solution of the even volume-normalized Lp-Minkowski problem was given for all p > 1.”
• Local Lp-Brunn-Minkowski inequalities for p<1 (2017, background): “local Lp-Brunn–Minkowski and log-Brunn–Minkowski inequalities into local uniqueness statements for the even Lp-Minkowski and log-Minkowski problems, respectively. The classical Minkowski problem (see [60, 51] and the references therein) asks for necessary and sufficient conditions on a finite Borel mea”
• The even Orlicz-Minkowski problem (2010, methodology): “In [40], it was shown that, for p 6= n, the Lp Minkowski problem (2) has an equivalent volume-normalized formulation and a solution of the even volume-normalized Lp Minkowski problem was given for all p > 1.”
• More on logarithmic sums of convex bodies (2014, background): “[31] [32] [33] [34] [35]), much less seem to be known for 0 ≤ p < 1.”
• Volume inequalities for isotropic measures (2006, background): “, [710,13-27,29-32,34,35,37]) none of the machinery of the theory is used.”
• The dual Minkowski problem for negative indices (2017, background): “sure so that it is exactly the Lp surface area measure of a convex body. The solution to the Lp Minkowski problem when p &gt; 1 was given by Chou &amp; Wang [12]. See also Chen [11], Lutwak [31], LYZ [35], and Zhu [51]. The solution to the Lp Minkowski problem has proven to be essential in establish”