## View abstract

### Session S38 - Geometric Potential Analysis

Friday, July 16, 19:35 ~ 20:05 UTC-3

## From affine Poincaré inequalities to affine spectral inequalities

We develop the basic theory of $p$-Rayleigh quotients in bounded domains, in the affine case, for $p \geq 1$. We establish $p$-affine versions of the affine Poincaré inequality and introduce the affine invariant $p$-Laplace operator $\Delta_p^{\mathcal A}$ defining the Euler-Lagrange equation of the minimization problem. For $p=1$ we obtain the existence of affine Cheeger sets and study preliminary results towards a possible spectral characterization of John's position.