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초록· 키워드
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Let C be a closed convex set in Sm or Hm. Assume that ∑ is an n-dimensional compact minimal submanifold outside C such that ∑ is orthogonal to ∂C along ∂∑ ∩ ∂C and ∂∑ lies on a geodesic sphere centered at a fixed point p ∈ ∂∑ ∩ ∂C and that r is the distance in Sm or Hm from p. We make use of a modified volume Mp(∑) of ∑ and obtain a sharp relative isoperimetric inequality ½nnωnMp(∑)n-1 ≤ Vol(∂∑ ~ ∂C)n,where ωn is the volume of a unit ball in Rn. Equality holds if and only if ∑ is a totally geodesic half ball centered at p.
목차
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참고문헌 (9)
참고문헌 신청
C. Bandle / 1980 / Isoperimetric inequalities and applications / Pitman
I. Kim / 1998 / Relative isoperimetric inequality and linear isoperimetric inequality for minimal submanifolds / Manuscripta Math. 97 : 343 ~ 352
J. Choe / 1992 / Isoperimetric inequalities on minimal submanifolds of space forms / Manuscripta Math. 77 : 169 ~ 189
J. Choe / 2003 / Relative isoperimetric inequality for domains outside a convex set / Arch. Inequal. Appl. 1 : 241 ~ 250
J. Choe / 2006 / The double cover relative to a convex set and the relative isoperimetric inequality / J. Aust. Math. Soc. 80 : 375 ~ 382
I. Kim / 1998 / Relative isoperimetric inequality and linear isoperimetric inequality for minimal submanifolds / Manuscripta Math. 97 : 343 ~ 352
J. Choe / 1992 / Isoperimetric inequalities on minimal submanifolds of space forms / Manuscripta Math. 77 : 169 ~ 189
J. Choe / 2003 / Relative isoperimetric inequality for domains outside a convex set / Arch. Inequal. Appl. 1 : 241 ~ 250
J. Choe / 2006 / The double cover relative to a convex set and the relative isoperimetric inequality / J. Aust. Math. Soc. 80 : 375 ~ 382
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