Contravariantly finite resolving subcategories of the category of finitely
generated modules have been playing an important role in the representation
theory of algebras. In this paper we study contravariantly finite resolving
subcategories over commutative rings. The main purpose of this paper is to
classify contravariantly finite resolving subcategories over a henselian
Gorenstein local ring; in fact there exist only three ones. Our method to
obtain this classification also recovers as a by-product the theorem of
Christensen, Piepmeyer, Striuli and Takahashi concerning the relationship
between the contravariant finiteness of the full subcategory of totally
reflexive modules and the Gorenstein property of the base ring.