102 citations · 498 across the 36 of their papers we have counts for
37 papers
Higher-Order Lp Isoperimetric and Sobolev Inequalities
Julián Haddad, Dylan Langharst, Eli Putterman +2
Schneider introduced an inter-dimensional difference body operator on convex bodies and proved an associated inequality. In the prequel to this work, we showed that this concept ca…
On the -Order Weighted Projection Body Operator and Related Inequalities
Dylan Langharst, Eli Putterman, Michael Roysdon +1
For a convex body in , the inequalities of Rogers-Shephard and Zhang, written succinctly, are $$\text{vol}_n(DK)\leq \binom{2n}{n} \text{vol}_n(K) \leq \text{vol}_…
Affine Isoperimetric Inequalities for Higher-Order Projection and Centroid Bodies
Julián Haddad, Dylan Langharst, Eli Putterman +2
In 1970, Schneider introduced the th order difference body of a convex body, and also established the th-order Rogers-Shephard inequality. In this paper, we extend this idea…
On the sine polarity and the -sine Blaschke-Santaló inequality
Qingzhong Huang, Ai-Jun Li, Dongmeng Xi +1
This paper is dedicated to study the sine version of polar bodies and establish the -sine Blaschke-Santaló inequality for the -sine centroid body. The -sine centroid…
On the Brunn-Minkowski theory and the Minkowski problem for -coconvex sets
Jin Yang, Deping Ye, Baocheng Zhu
Let be a pointed closed convex cone in with vertex at the origin and having nonempty interior. The set is -coconvex if the volume of is f…
Ulam floating functions
Chunyan Liu, Elisabeth M. Werner, Deping Ye +1
We extend the notion of Ulam floating sets from convex bodies to Ulam floating functions. We use the Ulam floating functions to derive a new variational formula for the affine surf…