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We prove that the solution of the wave equation associated to the Grushin operator G = -Delta -vertical bar x vertical bar(2)partial derivative(2)(t) is bounded on L-P (Rn+1), with 1 < p < infinity, when vertical bar 1/p - 1/2 vertical bar < 1/n+2.

We study the semistability of Q vertical bar s, the universal quotient bundle on G(1,3) restricted to any smooth surface S (called congruence). Specifically, we deduce geometric conditions for a congruence S, depending on the slope of a saturated linear subsheaf of Q vertical bar s. Moreover, we check that the Dolgachev-Reider Conjecture (i.e. the semistability of Q vertical bar s for nondegenerate congruences S) is true for all the congruences of degree less than or equal to 10. Also, when the degree of a congruence S is less than or equal to 9, we compute the highest slope reached by the linear subsheaves of Q vertical bar s.