The Collaborative International Dictionary of English v.0.48:

Concave \Con"cave\, v. t. [imp. & p. p. concaved; p. pr. & vb.
   n. Concaving.]
   To make hollow or concave.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Concave \Con"cave\ (k[o^][ng]*k[=a]*v" or k[o^]n"-; 277), a. [L.
   concavus; con- + cavus hollow: cf. F. concave. See Cave a
   hollow.]
   1. Hollow and curved or rounded; vaulted; -- said of the
      interior of a curved surface or line, as of the curve of
      the of the inner surface of an eggshell, in opposition to
      convex; as, a concave mirror; the concave arch of the
      sky.
      [1913 Webster]

   2. Hollow; void of contents. [R.]
      [1913 Webster]

            As concave . . . as a worm-eaten nut. --Shak.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Concave \Con"cave\, n. [L. concavum.]
   1. A hollow; an arched vault; a cavity; a recess.
      [1913 Webster]

            Up to the fiery concave towering hight. --Milton.
      [1913 Webster]

   2. (Mech.) A curved sheath or breasting for a revolving
      cylinder or roll.
      [1913 Webster]

WordNet (r) 3.0 (2006):

concave
    adj 1: curving inward [ant: bulging, convex]