• Corpus ID: 245669035

Homogeneous functions with nowhere vanishing Hessian determinant

  title={Homogeneous functions with nowhere vanishing Hessian determinant},
  author={Connor Mooney},
. We prove that functions that are homogeneous of degree α ∈ (0 , 1) on R n and have nowhere vanishing Hessian determinant cannot change sign. 
2 Citations

Figures from this paper

Gradient estimates for the Lagrangian mean curvature equation with critical and supercritical phase

. In this paper, we prove interior gradient estimates for the Lagrangian mean curvature equation, if the Lagrangian phase is critical and supercritical and C 2 . Combined with the a priori interior


Thesis: on a Rod Like Polyelectrolyte Model” RESEARCH Computational Systems Biology & Bioinformatics including the development of algorithms and their application to proteomes for the prediction of



Linearity of homogeneous order‐one solutions to elliptic equations in dimension three

We prove that any homogeneous order one solution to 3-d nondivergence elliptic equations must be linear.

Hessian and gradient estimates for three dimensional special Lagrangian equations with large phase

<abstract abstract-type="TeX"><p>We obtain a priori interior Hessian and gradient estimates for special Lagrangian equations with phase larger than a critical value in dimension three. Gradient

Global invertibility of Sobolev functions and the interpenetration of matter

  • J. Ball
  • Mathematics
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 1981
Synopsis A global inverse function theorem is established for mappings u: Ω → ℝn, Ω ⊂ ℝn bounded and open, belonging to the Sobolev space W1.p(Ω), p > n. The theorem is applied to the pure

Uniqueness results for the Minkowski problem extended to hedgehogs

AbstractThe classical Minkowski problem has a natural extension to hedgehogs, that is to Minkowski differences of closed convex hypersurfaces. This extended Minkowski problem is much more difficult

Dirichlet duality and the nonlinear Dirichlet problem

We study the Dirichlet problem for fully nonlinear, degenerate elliptic equations of the form F(Hess u) = 0 on a smoothly bounded domain Ω ⋐ ℝn. In our approach the equation is replaced by a subset F

Comparison principles for viscosity solutions of elliptic branches of fully nonlinear equations independent of the gradient

The validity of the comparison principle in variable coefficient fully nonlinear gradient free potential theory is examined and then used to prove the comparison principle for fully nonlinear partial

Space mappings with bounded distortion

Introduction Some facts from the theory of functions of a real variable Functions with generalized derivatives Mobius transformations Definition of a mapping with bounded distortion Mappings with

On mappings with integrable dilatation

A factorization of Stoilow's type has been obtained for mappings in R2 with integrable dilatation. 0. INTRODUCTION For Q a domain in Rn (an open and connected set), we consider a mapping -f Rn of the