Geodesic
On A.\,V.~Malyshev's approach to Minkowski's conjecture concerning the critical determinant of the region $|x|^p + |y|^p 1$ for $p > 1$
Čebyševskij sbornik, Tome 17 (2016) no. 4, pp. 185-193

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We present A. V. Malyshev's approach to Minkowski's conjecture (in Davis's amendment) concerning the critical determinant of the region $|x|^p + |y|^p 1$ for $p > 1$ and Malyshev's method. In the sequel of this article we use these approach and method to obtain the main result. Bibliography: 21 titles.
Keywords: critical lattice; critical determinant; Diophantine inequality; Diophantine approximation; distance function; star body; moduli space. 
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     author = {N. M. Glazunov},
     title = {On {A.\,V.~Malyshev's} approach to {Minkowski's} conjecture concerning the critical determinant of the region $|x|^p + |y|^p < 1$ for $p > 1$},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {185--193},
     publisher = {mathdoc},
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N. M. Glazunov. On A.\,V.~Malyshev's approach to Minkowski's conjecture concerning the critical determinant of the region $|x|^p + |y|^p < 1$ for $p > 1$. Čebyševskij sbornik, Tome 17 (2016) no. 4, pp. 185-193. http://geodesic.mathdoc.fr/item/CHEB_2016_17_4_a14/