EXCISION OF OS LUNATUM IN THE TREATMENT OF LUNATOMALACIA

The small size of Os lunatum and its nature as an articulation element which movement is similar to that of a "tank track" reduces the opportunities for free functioning of the radiocarpal joint after lunate damage. During a 15-year period (1982-1997) a total of 13 patients underwent an excision of Os lunatum. They were 9 males and 4 females aged between38 and 60 years (mean age of 41 years and 3 months). Eight patients were at 111A stage after Lichtman, two - at II1Ð’, and three - at IV stage of the disease. Intercarpal arthodesis after O. Craner (1966) was additionally performed in 9 patients after extirpation  of Os lunatum under conditions of a severe lunate collapse. A good result (of 22-26 scores) was obtained in seven patients, a satisfactory' one (of 13-15 scores) - in 3 patients but a poor one (below 8 scores) in 2 patients only. The good results after the application of the excision and particularly of the resection of Os lunatum proved the appropriateness of this method for the treatment of Kienhocks's disease at stages III and IV in case of absent arthrotic alterations of radius, Os capitatum, and Os scaphoideum. The intercarpal arthodesis ensured anaesthesia and carpal stablility despite a certain restriction of range of motion

ASEPTIC NECROSES OF CARPAL BONES

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One-phase free boundary solutions of finite Morse index

We study global solutions to the classical one-phase free boundary problem that have finite Morse index relative to the Alt-Caffarelli functional. We show that such solutions are stable outside a compact set and characterize the index as the maximal number of linearly independent $L^2$ integrable eigenfunctions of the corresponding Robin eigenvalue problem, associated to negative eigenvalues. As an application, we obtain a complete classification of global solutions of finite Morse index in the plane. Our results are counterparts to the minimal surface theorems of Fischer-Colbrie and Gulliver.Comment: 21 page

Structure of One-Phase Free Boundaries in the Plane

We study classical solutions to the one-phase free boundary problem in which the free boundary consists of smooth curves and the components of the positive phase are simply connected. We characterize the way in which the curvature of the free boundary can tend to infinity. Indeed, if curvature tends to infinity, then two components of the free boundary are close, and the solution locally resembles an entire solution discovered by Hauswirth, Hélein, and Pacard, whose free boundary has the shape of a double hairpin. Our results are analogous to theorems of Colding and Minicozzi characterizing embedded minimal annuli, and a direct connection between our theorems and theirs can be made using a correspondence due to Traizet.National Science Foundation (U.S.) (Grant DMS-1069225