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- CONTENTS 1989 - VOLUME 308 - SECTION I - N° 19
- .......... Page(s) .......... 543
- .......... Page(s) .......... 543
- If G is a locally compact second countable group and
(G), we investigate conditions under which the closed linear span of the set of left and right translates of by G is all of L2 (G); the conditions are that in the decomposition of L2 (G) over the centre of the von Neumann algebra generated by left G-translations, almost all components of are non-zero. - Our methods are also readily adapted to treat the case of the closed linear span of left G-translates of a vector in L2 (G/ K), whenever (G, K) is a Gelfand pair.
- We give an existence theorem for image segmentations obtained by minimizing the functional
- over closed subsets K of an open rectangle, with Hausdorff length , and over represents the "contours" of the image g and u its regularized version in the connected components of \K. This theorem is obtained by proving an equivalence between the above formulation and a new one proposed by De Giorgi and his school under the name of "free discontinuity problems". We also introduce a more computational version of the problem, where K is imposed to be the union of m curves, and show that this last formulation is asymptotically equivalent to both preceding formulations as m tends to infinity.
- .......... Page(s) .......... 555
- We give some boundary regularity results for the solutionos of a class of nonlinear degenerate parabolic equations in non-cylindrical domains.
- We establish the existence of a solution with convex level lines of a class of semilinear elliptic equations of the form where f (t) is positive and integrable. Our method is to construct the solution as a limit of a sequence of n free boundary problems where the n-th free boundary problem has n free boundaries.
- .......... Page(s) .......... 565
- .......... Page(s) .......... 565
- Let (M, g) be a compact, connected, oriented 2 n-dimensional Riemannian manifold, the twistor space t: of which has an integrable canonical almost-complex structure. If the complexified variety ZM (defined § 3.2) is compact (in particular, if Z (M) belongs to Fujiki's class C) then . Hence: if g is conformally flat, (M, g) is conformally equivalent to the standard S2n; if g is anti-self-dual and n=2, M is homeomorphic either to S4, or to the connected sum of copies of P2 (C). These results (§ 3) are deduced from more general results (§ 1 and 2).
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