Curvature and dimension
Examples of spaces with branching geodesics satisfying the curvature-dimension condition
... See [RS] for the precise statement. Our example (D 2 , d H , m L ) in (2.1) satisfies the hypothesis of Theorem 2.2, thus it shows that geodesics still can branch in this kind of essentially non-branching spaces. An ...
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The Li-Yau inequality and applications under a curvature-dimension condition
... This work is organised as follows. In the next section we state this gen- eralisation, for a Markov diffusion semigroup under a CD(ρ, n) curvature- dimension condition. We also derive first consequences, ...
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Submanifolds of Dimension in a Quaternionic Projective Space under Some Curvature Conditions
... The purpose of this paper is to study n-dimensional QR-submanifolds of (𝑝 − 1) QR-dimension in a quaternionic projective space QP (𝑛+𝑝)/4 and especially to determine such submanifolds under some curvature ...
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Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality
... As we will see in this work, this curvature dimension inequality may also be used to prove the Poincaré inequality, the log-Sobolev inequality or the Gaussian logarithmic isoperimetric i[r] ...
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CiteSeerX — SCALAR CURVATURE AND Q-CURVATURE OF RANDOM METRICS.
... the curvature perturbation is isotropic, so that in particular the variance is ...of dimension N m = 2m + 1 associated to the eigenvalue E m = m(m + 1), and for every m fix an L 2 orthonormal basis B m = {η ...
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and curvature measures
... x critical (−1) index (x) . Now suppose that M n−1 is a closed, oriented, and immersed submanifold of di- mension n − 1 in an oriented non-euclidean space Y n of constant curvature λ = ²K (where ² = ±1 and K is a ...
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Motion of hypersurfaces by curvature
... the curvature at a ...of dimension two, or the flow speed is a convex function of the ...garten curvature operator is asymptotically non-negative at a ...Weingarten curvature), the Weingarten ...
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Probability and Curvature in Physics
... Later Einstein constructed some unified field models that regarded electromagnetic field as curved space-time structure: he followed Klein-Kaluza theory at the beginning, and treated electromagnetic field as the 5 th ...
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Q curvature and gravity
... The fundamental building block to construct the action of the theory will be the so-called Q- curvature, which is an important notion of conformal geometry [15, 16]. Originally introduced by Branson in [17], the ...
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Convexity and curvature in Lorentzian geometry
... mean curvature vector field is causal and future-pointing is called a weakly future-trapped ...arbitrary dimension with closed trapped submanifolds of arbitrary co-dimension ...
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CiteSeerX — EXOTIC SPHERES AND CURVATURE
... Hern´ andez-Andrade’s approach is to consider the metrics induced on Brieskorn manifolds from the ambient Euclidean metric. Since the Brieskorn manifolds can be described entirely by polynomial equations, one can write ...
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ON THE COMPARISON OF STATISTICAL CURVATURE WITH GAUSSIAN CURVATURE
... statistical curvature to measure the shape of a one-parameter exponential ...statistical curvature with the classical Gaussian ...defined curvature has greatly reduced the quantities of ...
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Curvature of Transport
... curv tra : P n+1 (X) → T n+1 . The functor tra is flat precisely if curv tra is trivial on all (n + 1)-morphisms. For the special case that n = 1 and T = ΣG, with tra : P 1 (X) → ΣG coming from a 1-form A as in prop. ??, ...
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, the formula for the curvature (and radius of curvature) is stated in all calculus textbooks
... For the above example the circle of curvature was easy to locate because it's center lies on the y-axis. How do you locate the center if the point of tangency is not the origin? To begin, we need the concepts of ...
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CiteSeerX — Conformal metrics with prescribed curvature curvature functions on manifolds with boundary
... FUNCTIONS ON MANIFOLDS WITH BOUNDARY By B O G UAN Dedicated to Professor Joel Spruck on the occasion of his 60th birthday. Abstract. We study the Dirichlet problem for a class of fully nonlinear elliptic equations ...
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COMPUTING CURVATURE AND CURVATURE NORMALS ON SMOOTH LOGICALLY CARTESIAN SURFACE MESHES
... The Euler spiral is then (C(t), S(t)). It can be shown that the curvature is κ = 2t, where t is the arc-length. As t → ∞ then κ → ∞ giving two points around which the spiral infinitely winds. As t gets large, ...
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On the Curvature of Rotating Objects
... plays the role of mass-energy in the system under study. If it is really a property of Lorentz geometry that rotat- ing objects may have lower energy than non-rotating ones, this would imply a picture where rotating ...
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Membrane curvature at a glance
... Journal of Cell Science Introduction The formation of many intracellular membrane compartments allows the cell to compartmentalize proteins, thereby supporting the complex and timely coordination of the thousands of ...
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Varifolds and generalized curvature
... Obviously, this problem depends on the hypothesis on Γ, the set of surfaces one authorizes and the meaning one gives to span. In 1931 (cf. [5]), J. Douglas solved the problem in the restricted class of surfaces being ...
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EXTENSIONS OF CONSTANT CURVATURE
... In each case it may be noted that the Christoffel symbols and hence the geodesic equa- tions are extended. We give examples where extension of flat metric is flat and that of extension of a metric of non zero constant ...
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