Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a version of the slicing problem for the surface area of convex
  bodies   We study the slicing inequality for the surface area instead of volume. This
is the question whether there exists a constant $\alpha_n$ depending (or not)
on the dimension $n$ so that $$S(K)\leq\alpha_n|K|^{\frac{1}{n}}\max_{\xi\in
S^{n-1}}S(K\cap\xi^{\perp })$$ where $S$ denotes surface area and $|\cdot |$
denotes volume. For any fixed dimension we provide a negative answer to this
question, as well as to a weaker version in which sections are replaced by
projections onto hyperplanes. We also study the same problem for sections and
projections of lower dimension and for all the quermassintegrals of a convex
body. Starting from these questions, we also introduce a number of natural
parameters relating volume and surface area, and provide optimal upper and
lower bounds for them. Finally, we show that, in contrast to the previous
negative results, a variant of the problem which arises naturally from the
surface area version of the equivalence of the isomorphic Busemann--Petty
problem with the slicing problem has an affirmative answer.

21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys