Abstract: Among other things, a heart tissue support has gripping elements, each element having a free end that is sharp enough to penetrate heart tissue when pushed against the tissue, and a feature to resist withdrawal from the tissue after the sharp free end has penetrated the tissue. Among other things, the shape of a heart valve annulus is corrected in a catheter laboratory by orienting a tip of a catheter holding a heart tissue support that has gripping elements at the valve annulus, applying a radial force from the catheter against the annulus by opening a structure at the tip of the catheter, and while the structure is opened, forcing the support onto the annulus. Among other things, the shape of a heart valve annulus is corrected during a surgical procedure by pushing a heart tissue support that has gripping elements onto the annulus.