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• W2767687749 abstract "We show that the linear drift of the Brownian motion on the universal cover of a closed connected smooth Riemannian manifold is <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C Superscript k minus 2> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>k</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:annotation encoding=application/x-tex>C^{k-2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> differentiable along any <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C Superscript k> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>k</mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding=application/x-tex>C^{k}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> curve in the manifold of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C Superscript k> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mi>k</mml:mi> </mml:msup> <mml:annotation encoding=application/x-tex>C^k</mml:annotation> </mml:semantics> </mml:math> </inline-formula> Riemannian metrics with negative sectional curvature. We also show that the stochastic entropy of the Brownian motion is <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C Superscript 1> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>1</mml:mn> </mml:msup> <mml:annotation encoding=application/x-tex>C^1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> differentiable along any <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C cubed> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> <mml:annotation encoding=application/x-tex>C^{3}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> curve of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C cubed> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>3</mml:mn> </mml:msup> <mml:annotation encoding=application/x-tex>C^3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> Riemannian metrics with negative sectional curvature. We formulate the first derivatives of the linear drift and stochastic entropy, respectively, and show they are critical at locally symmetric metrics." @default.
• W2767687749 created "2017-11-17" @default.
• W2767687749 creator A5002160599 @default.
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• W2767687749 date "2023-01-01" @default.
• W2767687749 modified "2023-10-15" @default.
• W2767687749 title "The Regularity of the Linear Drift in Negatively Curved Spaces" @default.
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• W2767687749 doi "https://doi.org/10.1090/memo/1387" @default.
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