Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mappings of preserving $n$-distance one in $n$-normed spaces   We give a positive answer to the Aleksandrov problem in $n$-normed spaces
under the surjectivity assumption. Namely, we show that every surjective
mapping preserving $n$-distance one is affine, and thus is an $n$-isometry.
This is the first time to solve the Aleksandrov problem in $n$-normed spaces
with only surjective assumption even in the usual case $n=2$. Finally, when the
target space is $n$-strictly convex, we prove that every mapping preserving two
$n$-distances with an integer ratio is an affine $n$-isometry.

13
The categories of this paper are: quant-ph
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The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph