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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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We give area and height estimates for cmc-graphs over a bounded planar C2,α domain ⊂ R3. For a constant H satisfying H2|Ω|≤ 9π/16, we show that the height h of H-graphs over with vanishing boundary satisfies |h| < (˜r/2π)H|Ω|, where ˜r is the middle zero of (x−1)(H2|Ω|(x+2)2 −9π(x−1)). We use this height estimate to prove the following existence result for cmc H-graphs: for a constant H satisfying H2|Ω| < (297 − 13)π/8, there exists an H-graph with vanishing boundary.
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참고문헌 (15)
참고문헌 신청
D. Gilbarg / 2001 / Elliptic Partial Differential Equations of Second Order / Springer-Verlag
E. Heinz / 1969 / On the nonexistence of a surface of constant mean curvature with finite area and prescribed rectifiable boundary / Arch. Rational Mech. Anal 35 : 249 ~ 252
F. Morgan / 2000 / Geometric Measure Theory, A beginner’s guide, Third edition / Academic Press, Inc.
H. Wente / 1969 / An existence theorem for surfaces of constant mean curvature / J. Math. Anal. Appl 26 : 318 ~ 344
J. McCuan / 1999 / Continua of H-graphs: convexity and isoperimetric stability / Calc. Var. Partial Differential Equations 9 (4) : 297 ~ 325
E. Heinz / 1969 / On the nonexistence of a surface of constant mean curvature with finite area and prescribed rectifiable boundary / Arch. Rational Mech. Anal 35 : 249 ~ 252
F. Morgan / 2000 / Geometric Measure Theory, A beginner’s guide, Third edition / Academic Press, Inc.
H. Wente / 1969 / An existence theorem for surfaces of constant mean curvature / J. Math. Anal. Appl 26 : 318 ~ 344
J. McCuan / 1999 / Continua of H-graphs: convexity and isoperimetric stability / Calc. Var. Partial Differential Equations 9 (4) : 297 ~ 325
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