Kinematic formulas of total mean curvatures for hypersurfaces

Ming Li , Jiazu Zhou

Chinese Annals of Mathematics, Series B ›› 2016, Vol. 37 ›› Issue (1) : 137 -148.

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Chinese Annals of Mathematics, Series B ›› 2016, Vol. 37 ›› Issue (1) : 137 -148. DOI: 10.1007/s11401-015-0952-2
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Kinematic formulas of total mean curvatures for hypersurfaces

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Abstract

By using the moving frame method, the authors obtain a kind of asymmetric kinematic formulas for the total mean curvatures of hypersurfaces in the n-dimensional Euclidean space.

Keywords

Kinematic formula / Total mean curvature / Hypersurface

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Ming Li, Jiazu Zhou. Kinematic formulas of total mean curvatures for hypersurfaces. Chinese Annals of Mathematics, Series B, 2016, 37(1): 137-148 DOI:10.1007/s11401-015-0952-2

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References

[1]

Chen C.-S.. On the kinematic formula of square of mean curvature. Indiana Univ. Math, 1972, 22: 1163-1169

[2]

Chern S. S.. On integral geometry in Klein spaces. Ann. of Math, 1942, 43(2): 178-189

[3]

Chern S. S.. On the kinematic formula in the Euclidean space of n dimensions. Amer. J. Math, 1952, 74: 227-236

[4]

Chern S. S.. On the kinematic formula in integral geometry. J. Math. and Mech, 1966, 16(1): 101-118

[5]

Chern S. S., Chen W., Lam K. S.. Lectures on Differential Geometry. Series on Univ. Math., 1999, Singapore: World Scientific

[6]

Gallego E., Naveira A. M., Solanes G.. Horospheres and convex bodies in n-dimensional hyperbolic space. Geom. Dedicata, 2004, 103: 103-114

[7]

Howard R.. The kinematic formula in Riemannian homogeneous spaces. Mem. Amer. Math. Soc, 1993, 509: 1-69

[8]

Jiang D., Zhou J., Chen F.. A kinematic formula for integral invariant of degree 4 in real space form. Acta Math. Sin. (Engl. Ser.), 2014, 30(8): 1465-1476

[9]

Klain D.. Bonnesen-type inequalities for surfaces of constant curvature. Adv. Appl. Math, 2007, 39: 143-154

[10]

Li M., Zhou J.. An isoperimetric deficit upper bound of the convex domain in a surface of constant curvature. Sci. China Math, 2010, 53(8): 1941-1946

[11]

Ren D.. Topics in Integral Geometry, 1994, Singapore: World Scientific

[12]

Santaló L. A.. Integral Geometry and Geometric Probability, 2004, Cambridge: Cambridge University Press

[13]

Solanes G.. Integral geometry of equidistants in hyperbolic spaces. Israel J. Math, 2005, 145: 271-284

[14]

Weyl H.. On the volume of tubes. Amer. J. Math, 1939, 61: 461-472

[15]

Xia Y., Xu W., Zhou J., Zhu B.. Reverse Bonnesen style inequalities in a surface X2e of constant curvature. Sci. China Math, 2013, 56(6): 1145-1154

[16]

Zhou J.. A kinematic formula and analogues of Hadwiger’s theorem in space. Contemp. Math, 1992, 140: 159-167

[17]

Zhou J.. The sufficient condition for a convex body to enclose another in R4. Proc. Amer. Math. Soc, 1994, 121(3): 907-913

[18]

Zhou J.. Kinematic formulas for mean curvature powers of hypersurfaces and Hadwiger’s theorem in R2n. Trans. Amer., Math., Soc, 1994, 345(1): 243-262

[19]

Zhou J.. On the Willmore deficit of convex surfaces, Tomography, Impedance Imaging, and Integral Geometry. Lectures in Appl. Math., 1994, 30: 279-287

[20]

Zhou J.. When can one domain enclose another in R3?. J. Austral. Math. Soc. (Ser. A), 1995, 59(2): 266-272

[21]

Zhou J.. Sufficient conditions for one domain to contain another in a space of constant curvature. Proc. Amer. Math. Soc, 1998, 126(9): 2797-2803

[22]

Zhou J.. The Willmore functional and the containment problem in R4. Sci. China Ser. A, 2007, 50(3): 325-333

[23]

Zhou J.. On Willmore inequality for submanifolds. Canad. Math. Bull, 2007, 50(3): 474-480

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