N. M. Ivochkina, “From Gårding's cones to $p$-convex hypersurfaces”, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 1, CMFD, 45, PFUR, M., 2012, 94–104; Journal of Mathematical Sciences, 201:5 (2014), 634

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Contemporary Mathematics. Fundamental Directions

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Contemporary Mathematics. Fundamental Directions, 2012, Volume 45, Pages 94–104 (Mi cmfd215)

This article is cited in 6 scientific papers (total in 7 papers)

From Gårding's cones to

$p$ -convex hypersurfaces

N. M. Ivochkina

St. Petersburg State University of Architecture and Civil Engineering, St. Petersburg, Russia

Full-text PDF (180 kB) Citations (7)

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Abstract: We consider cones discovered by Gårding in 1959. They play the fundamental role in the modern theory of fully nonlinear second-order partial differential equations. A new classification of symmetric matrices is presented based on the

$m$ -positiveness property. Such a classification establishes a new trend in geometry, generating a notion of

$m$ -convex hypersurfaces.

English version:
Journal of Mathematical Sciences, 2014, Volume 201, Issue 5, Pages 634–644
DOI: https://doi.org/10.1007/s10958-014-2016-7

Bibliographic databases:

Document Type: Article

UDC: 517.957

Language: Russian

Citation: N. M. Ivochkina, “From Gårding's cones to

$p$ -convex hypersurfaces”, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 1, CMFD, 45, PFUR, M., 2012, 94–104; Journal of Mathematical Sciences, 201:5 (2014), 634–644

Citation in format AMSBIB

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\by N.~M.~Ivochkina

\paper From G\aa rding's cones to $p$-convex hypersurfaces

\inbook Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14--21, 2011). Part~1

\serial CMFD

\yr 2012

\vol 45

\pages 94--104

\publ PFUR

\publaddr M.

\mathnet{http://mi.mathnet.ru/cmfd215}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3087053}

\transl

\jour Journal of Mathematical Sciences

\yr 2014

\vol 201

\issue 5

\pages 634--644

\crossref{https://doi.org/10.1007/s10958-014-2016-7}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84905873879}

Linking options:

https://www.mathnet.ru/eng/cmfd215

https://www.mathnet.ru/eng/cmfd/v45/p94

This publication is cited in the following 7 articles:

N. M. Ivochkina, S. I. Prokof'eva, G. V. Yakunina, “Integral Inequalities in the Theory of Hessian Operators”, Math. Notes, 109:4 (2021), 570–579
Gang Li, Saihua Cui, Feida Jiang, “Inclusion Relations of Gårding's Cones and k-Convex Cones”, Bull. Malays. Math. Sci. Soc., 43:1 (2020), 125
A. A. Borisenko, A. Yu. Vesnin, N. M. Ivochkina, “On the 100th anniversary of the birth of Aleksei Vasil'evich Pogorelov”, Russian Math. Surveys, 74:6 (2019), 1135–1157
N. V. Filimonenkova, “Geometriya $m$ -gessianovskikh uravnenii”, Materialy mezhdunarodnoi konferentsii “Geometricheskie metody v teorii upravleniya i matematicheskoi fizike”, posvyaschennoi 70-letiyu S.L. Atanasyana, 70-letiyu I.S. Krasilschika, 70-letiyu A.V. Samokhina, 80-letiyu V.T. Fomenko. Ryazanskii gosudarstvennyi universitet im. S.A. Esenina, Ryazan, 25–28 sentyabrya 2018 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 169, VINITI RAN, M., 2019, 98–115
N. M. Ivochkina, N. V. Filimonenkova, “Konusy Gordinga i uravneniya Bellmana v teorii gessianovskikh operatorov i uravnenii”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 63, no. 4, Rossiiskii universitet druzhby narodov, M., 2017, 615–626
N. M. Ivochkina, N. V. Filimonenkova, “On new structures in the theory of fully nonlinear equations”, Journal of Mathematical Sciences, 233:4 (2018), 480–494
N. M. Ivochkina, N. V. Filimonenkova, “On algebraic and geometric conditions in the theory of Hessian equations”, J. Fixed Point Theory Appl., 16:1-2 (2014), 11

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	59

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