The phrase "applications in geometry of" is correct and usable in written English.
It can be used when discussing the practical uses or implications of geometric concepts in various fields or contexts.
Example: "The applications in geometry of advanced algorithms can significantly enhance computer graphics rendering."
Alternatives: "uses in geometry of" or "implications in geometry of".
Theorem A shows the asymptotic expression of the probabilistic widths of the identity embedding from R m into ℓ q m, 1 ≤ q ≤ 2. Theorem B gives the upper estimate of Gelfand numbers of operators from ℓ 1 m into a Hilbert space, and some of its striking applications in the geometry of Banach spaces and Rademacher processes can be found in [22].
Remark 1 (a) Theorem A shows the asymptotic expression of the probabilistic widths of the identity embedding from R m into ℓ q m, 1 ≤ q ≤ 2. (b) Theorem B gives the upper estimate of Gelfand numbers of operators from ℓ 1 m into a Hilbert space, and some of its striking applications in the geometry of Banach spaces and Rademacher processes can be found in [22].
That is true in "Geometry of Quiet," too.
Known nowadays as Ekeland's variational principle (in short, EVP), it has significant applications in the geometry theory of Banach spaces, optimization theory, game theory, optimal control theory, dynamical systems, and so forth; see [1 11] and references therein.
Blundon's inequality and Ciamberlini's inequality have many applications in Euclidean geometry, particularly in the field of geometric inequalities.
It would also be interesting to seek analogs of 1-harmonic applications in calibration geometry.
Dorin Andrica received his Ph.D in 1992 from "Babes¸-Bolyai" University in Cluj-Napoca, Romania; his thesis treated critical points and applications to the geometry of differentiable submanifolds.
Dorin Andrica received his Ph.D. in 1992 from "Babes-Bolyai" University in Cluj-Napoca, Romania; his thesis treated critical points and applications to the geometry of differentiable submanifolds.
