V.M. Miklyukov: from dimension 8 to nonassociative algebras

Abstract

In this short survey we give a background and explain some recent developments in algebraic minimal cones and nonassociative algebras. A good deal of this paper is recollections of my collaboration with my teacher, PhD supervisor and a colleague, Vladimir Miklyukov on minimal surface theory that motivated the present research. This paper is dedicated to his memory.

arXiv comment19 pages

References in corpus (8)

• Primitive axial algebras of Jordan type
• Universal Axial Algebras and a Theorem of Sakuma
• Minimal cubic cones via Clifford algebras
• Denjoy-Ahlfors Theorem for Harmonic Functions on Riemannian Manifolds and External Structure of Minimal Surfaces
• A correction of the decomposability result in a paper by Meyer-Neutsch
• A generalization of Cartan's theorem on isoparametric cubics
• Disjoint minimal graphs
• Spectral properties of nonassociative algebras and breaking regularity for nonlinear elliptic type PDEs

Cited by in corpus (2)

• Decomposition algebras and axial algebras
• Harmonic cubic homogeneous polynomials such that the norm-squared of the Hessian is a multiple of the Euclidean quadratic form