In this paper, we try to give a classification of spacelike hypersurfaces the Lorentz-Minkowski space-time E1n+1, whose mean curvature vector field order (k+ 1) is an eigenvector kth linearized operator Lk, for non-negative integer k less than n. The Lk defined as linear part first variation (k + 1)th hypersurface arising from its normal variations. We show that any E1n+1 satisfying condition L...

For an n-dimensional hypersurface in unit sphere, we introduce an abstract Willmore type called W (n,F)-Willmore functional, which generalizes the well-known classic Willmore functional. Its critical point is called the W (n,F)-Willmore hypersurface, for which the variational equation and Simons' type integral equalities are obtained. Moreover, we construct a few examples of W (n,F)-Willmore hy...

In this paper we introduce the concept of a bipolar variety of a real algebraic hypersurface. This notion is then used for the design and complexity estimations of a novel type of algorithms that finds algebraic sample point for the connected component of a singular real hypersurface. The complexity of these algorithms is polynomial in the maximal geometric degree of the bipolar varieties of th...

We give a full exceptional collection in the triangulated category of singularities in the sense of Orlov [16] for a hypersurface singularity of Fermat type, and discuss its relation with homological mirror symmetry for simple elliptic hypersurface singularities.

We determine the coefficients of the classes of highest weight in the conjugacy class expansion of the monomial symmetric polynomials evaluated at the Jucys-Murphy elements. We apply our result, along with other properties of Jucys-Murphy elements, to give streamlined derivations of the first-order asymptotics and character expansion of the Weingarten function for the unitary group.

Abstract We study U-DHOST theories, i.e., higher-order scalar-tensor theories which are degenerate only in the unitary gauge and yield an apparently unstable extra mode a generic coordinate system. show that satisfies three-dimensional elliptic differential equation on spacelike hypersurface, hence it does not propagate. clarify how to treat this “shadowy” at both linear nonlinear levels.

Here we prove a global existence theorem for the solutions of semi-linear wave equation with critical non-linearity admitting positive definite Hamiltonian. Formulating parametrix in globally hyperbolic curved spacetime, derive an apriori pointwise bound solution nonlinear terms initial energy, from which follows straightforward way. This is accomplished two steps. First, based on Moncrief's li...

Introduction. In my note on A 5 curve theorem generalizing the theorem of Carnot, I introduced the notion of curve cross ratio. This extension of the ordinary cross ratio is the simplest situationally invariant (3.4) case of the generalized or hypersurface cross ratio of n + l pairs of hypersurfaces in w-space which is the subject of the following lines. The generalized cross ratio is a t the s...