The intent of this book is to set the modern foundations of the theory of generalized curvature measures. This subject has a long history, beginning with J. Steiner (1850), H. Weyl (1939), H. Federer (1959), P. Wintgen (1982), and continues today with young and brilliant mathematicians. In the last decades, a renewal of interest in mathematics as well as computer science has arisen (finding new applications in computer graphics, medical imaging, computational geometry, visualization …).
This book deals with problems which are sufficiently important to become the subject of studies.
Cancer of the stomach remains one of the most pressing medical problems. Meanwhile,
scientific and practical interest in this problem has markedly diminished during recent years.
According to some experts, this can be explained first by the decreasing incidence of gastric
cancer. But this concerns only some developed countries, where effective measures are taken
for the prevention and early diagnosis of malignant tumors.
Invariant measures for the geodesic ﬂow on the unit tangent bundle of a negatively curved Riemannian manifold are a basic and well-studied subject. This paper continues an investigation into a 2-dimensional analog of this ﬂow for a 3-manifold N . Namely, the article discusses 2-dimensional surfaces immersed into N whose product of principal curvature equals a constant k between 0 and 1, surfaces which are called k-surfaces.
We study the large eigenvalue limit for the eigenfunctions of the Laplacian, on a compact manifold of negative curvature – in fact, we only assume that the geodesic ﬂow has the Anosov property. In the semi-classical limit, we prove that the Wigner measures associated to eigenfunctions have positive metric entropy. In particular, they cannot concentrate entirely on closed geodesics. 1.
We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative curvature geometry.
We study time variation in expected excess bond returns. We run regressions of
one-year excess returns on initial forward rates. We find that a single factor, a
single tent-shaped linear combination of forward rates, predicts excess returns on
one- to five-year maturity bonds with R2 up to 0.44. The return-forecasting factor is
countercyclical and forecasts stock returns. An important component of the returnforecasting
factor is unrelated to the level, slope, and curvature movements described
by most term structure models.