The Collaborative International Dictionary of English v.0.48:

Concavity \Con*cav"i*ty\, n.; pl. Concavities. [L. concavitas:
   cf. F. concavit['e]. See Concave.]
   A concave surface, or the space bounded by it; the state of
   being concave.
   [1913 Webster]

WordNet (r) 3.0 (2006):

concavity
    n 1: a shape that curves or bends inward [syn: concave shape,
         concavity, incurvation, incurvature]
    2: the property possessed by a concave shape [syn: concavity,
       concaveness]

Moby Thesaurus II by Grady Ward, 1.0:

118 Moby Thesaurus words for "concavity":
   aduncity, alveolation, alveolus, antrum, aquilinity, arching,
   arcuation, armpit, basin, boss, bowl, bump, cavity, circularity,
   colophon, concameration, concave, convexity, convolution, crater,
   crookedness, crypt, cup, curvation, curvature, curving, curvity,
   dactylogram, dactylograph, de-escalation, debasement, decurvation,
   decurvature, degradation, demotion, dent, depression, descent,
   detrusion, diminution, dint, dip, ducking, embossment, excrescence,
   excurvation, excurvature, fingerprint, fold, follicle, footmark,
   footprint, footstep, fossil footprint, funnel chest, hauling down,
   hole, hollow, hollow shell, hollowness, hookedness, ichnite,
   ichnolite, impress, impression, imprint, incurvation, incurvature,
   incurvity, indent, indentation, indention, lacuna, lowering, lump,
   pad, paw print, pawmark, pimple, pit, pocket, print, pug, pugmark,
   punch bowl, recurvation, recurvature, recurvity, reduction,
   rondure, rotundity, sag, scoop, seal, shell, sigil, signet, sink,
   sinkage, sinkhole, sinking, sinuosity, sinuousness, sinus, socket,
   stamp, step, stud, submergence, thrusting under, thumbmark,
   thumbprint, tortuosity, tortuousness, trough, vaulting, vestige,
   vug