In this paper we will explain an interesting phenomenon which occurs in general
nonassociative algebras. More precisely, we establish that any finite-dimensional …

In this paper, we address the following question: Why certain nonassociative algebra
structures emerge in the regularity theory of elliptic type PDEs and also in constructing …

The purpose of this paper is to give a systematic study of two new classes of commutative
nonassociative algebras, the so-called isospectral and medial algebras. An isospectral …

In their paper of 1993, Meyer and Neutsch established the existence of a 48-dimensional
associative subalgebra in the Griess algebra G. By exhibiting an explicit counter example …

The space of tensors of metric curvature type on a Euclidean vector space carries a two-
parameter family of orthogonally invariant commutative nonassociative multiplications …

If V is a finite-dimensional unital commutative (maybe nonassociative) algebra carrying an
associative positive definite bilinear form〈,〉 then there exist a nonzero idempotent c≠ e (e …

We prove a conjecture made by the first author: given an n-body central configuration X_0 in
the euclidean space R^{2p}, let Im F be the set of ordered real p-tuples …

We are interested in finding nonlinear polynomials $ P $ on $\mathbb {R}^ n $ that solves
the minimal surface equation. We first prove a structure theorem on such polynomials. We …

Understanding and finding of general algebraic constant mean curvature surfaces in the
Euclidean spaces is a hard open problem. The basic examples are the standard spheres …

We discuss what is known about homogeneous solutions $ u $ to the $ p $-Laplace
equation, $ p $ fixed, $1< p<\infty $, when $(A) u $ is an entire $ p $-harmonic function on …