7 problems

Let $(X,d)$ be a compact metric space, and let $d_I$ denote the intrinsic distance associated with $d$. The space is assumed to satisfy that $d_I(\cdot,x)$ has slope $1$ on…

Let $Z\subset\mathbb{R}^2$ be a rectifiable barrier, and define the minimum-time function by … where $R^Z(t)$ is the region reachable from the initial fire $R_0$ by absolutely cont…

Let $W$ be the distance map associated with a data-driven Finslerian car model on a Finsler manifold, let $\mathcal{F}^*$ be the dual Finsler function, and let $\mathbf{p}_0$ be th…

Let $u(x,y)=e^{ix}-e^{iy}$, where $e^{it}=(\cos t,\sin t)$, be the vectorial Eikonal boundary datum, let $\mathcal{O}$ be a domain with $0\notin\mathcal{O}$, and let…

Let $u(x,y)=(x^2+y^2)^{1/2}$ be the scalar Eikonal solution, let $\mathcal{O}$ be a domain with $0\notin\mathcal{O}$, and let $\sigma^\mathcal{O}$ denote the limiting measure assoc…

Gaussian decay conjecture. There exists a constant $\rho>0$ such that, for sufficiently small $h$,

Let $f$ be an eikonal polynomial of degree $g\geq 2$. A polynomial is isoparametric if it belongs to the isoparametric class, and it is primitive if it is congruent to a primitive…