let $\Omega \subset \mathbb{R}^{2}$ a domain,let $u \in C^{2}(\Omega)$, the operator
$Lu= tr(A.D^{2}u) + <\nabla u,b> +cu$
where $A$ is a symmetric matrix, $b$ is a vector field continuous on $\mathbb{R}^{n}$ and $c \in C(\Omega)$ is said uniformly elliptic if there exists constants $\lambda,\Lambda$, such that $\lambda \leq \Lambda$ where, for all $\xi \in \mathbb{R}^{n}$
$\lambda |\xi|^{2} \leq \xi^{t}A\xi \leq \Lambda |\xi|^{2}$ .
What is the the relation of the control of eingenvalues with the equation? What is the geometric interpretation for the uniformly elliptic equation? There is relation with curvature?
To me, being uniformly elliptical means having an ellipse trapped between two paraboloids, one with a smaller opening and one with a larger opening.