منابع مشابه
A Morse-Sard theorem for the distance function on Riemannian manifolds
We prove that the set of critical values of the distance function from a submanifold of a complete Riemannian manifold is of Lebesgue measure zero. In this way, we extend a result of Itoh and Tanaka.
متن کاملA new look at the Heston characteristic function
A new expression for the characteristic function of log-spot in Heston model is presented. This expression more clearly exhibits its properties as an analytic characteristic function and allows us to compute the exact domain of the moment generating function. This result is then applied to the volatility smile at extreme strikes and to the control of the moments of spot. We also give a factoriz...
متن کاملHessian of the Riemannian Squared Distance Function on Connected Locally Symmetric Spaces with Applications
Many optimization problems formulated on Riemannian manifolds involve their intrinsic Riemannian squared distance function. A notorious and important example is the centroid computation of a given finite constellation of points. In such setups, the implementation of the fast intrinsic Newton optimization scheme requires the availability of the Hessian of this intrinsic function. Here, a method ...
متن کاملOn the Area Distance and the Riemannian Geometry
In the standard cosmological model, one usually deals with the RobertsonWalker line element to describe various kinematical, dynamical or alchemical processes in the Universe. Although the observations refer to the high degree of homogeneity and isotropy of the Universe, current and future measurements would require theoretical models with a more general geometry of spacetime. A fundamental rol...
متن کاملThe Diameter and the Mean Distance of a Riemannian Manifold
Let M be a compact Riemannian manifold. For x, y G M, denote by p(x,y) the distance between x and y, i.e., the infimum of lengths of continuous piecewise C paths between x and y. (Notice that for geodesically complete manifolds there is always a path from x to y of length p(x,y).) The invariants of M based on the distance p are called metrical invariants. Most of them are related to the geometr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 2014
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2013.06.004