. "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . . . "000309169800008" . . . . "Rataj, Jan" . "Houston Journal of Mathematics" . . "38" . "P(GA201/09/0067), Z(MSM0021620839)" . "11320" . "Zaj\u00ED\u010Dek, Lud\u011Bk" . "CRITICAL VALUES AND LEVEL SETS OF DISTANCE FUNCTIONS IN RIEMANNIAN, ALEXANDROV AND MINKOWSKI SPACE" . . . . "[99EC626F0034]" . . . . "2"^^ . . "0362-1588" . . "129060" . . "RIV/00216208:11320/12:10126164!RIV13-GA0-11320___" . . "positive reach; DC manifold; Alexandrov space; Riemannian manifold; Minkowski space; finite dimensional Banach space; distance sphere; critical point; Distance function"@en . "Let F be a closed subset of R^n and n = 2 or n = 3. S. Ferry (1975) proved that then, for almost all r > 0, the level set (distance sphere, r-boundary) S^r(F) := {x is an element of R^n : dist(x, F) = r} is a topological (n - 1)-dimensional manifold. This result was improved by J.H.G. Fu (1985). We show that Ferry's result is an easy consequence of the only fact that the distance function d(x) = dist(x, F) is locally DC and has no stationary point in R^n\\F. Using this observation, we show that Ferry's (and even Fu's) result extends to sufficiently smooth normed linear spaces X with dim X is an element of {2, 3} (e.g., to l(n)(p), n = 2, 3, p }= 2), which improves and generalizes a result of R. Gariepy and W.D. Pepe (1972). By the same method we also generalize Fu's result to Riemannian manifolds and improve a result of K. Shiohama and M. Tanaka (1996) on distance spheres in Alexandrov spaces." . . . "CRITICAL VALUES AND LEVEL SETS OF DISTANCE FUNCTIONS IN RIEMANNIAN, ALEXANDROV AND MINKOWSKI SPACE" . . "2"^^ . "2" . "23"^^ . "CRITICAL VALUES AND LEVEL SETS OF DISTANCE FUNCTIONS IN RIEMANNIAN, ALEXANDROV AND MINKOWSKI SPACE"@en . . "Let F be a closed subset of R^n and n = 2 or n = 3. S. Ferry (1975) proved that then, for almost all r > 0, the level set (distance sphere, r-boundary) S^r(F) := {x is an element of R^n : dist(x, F) = r} is a topological (n - 1)-dimensional manifold. This result was improved by J.H.G. Fu (1985). We show that Ferry's result is an easy consequence of the only fact that the distance function d(x) = dist(x, F) is locally DC and has no stationary point in R^n\\F. Using this observation, we show that Ferry's (and even Fu's) result extends to sufficiently smooth normed linear spaces X with dim X is an element of {2, 3} (e.g., to l(n)(p), n = 2, 3, p }= 2), which improves and generalizes a result of R. Gariepy and W.D. Pepe (1972). By the same method we also generalize Fu's result to Riemannian manifolds and improve a result of K. Shiohama and M. Tanaka (1996) on distance spheres in Alexandrov spaces."@en . . . . "CRITICAL VALUES AND LEVEL SETS OF DISTANCE FUNCTIONS IN RIEMANNIAN, ALEXANDROV AND MINKOWSKI SPACE"@en . "RIV/00216208:11320/12:10126164" . .