عنوان

Strictly convex submanifolds and hypersurfaces of positive curvature

شماره

TLpq304419058

زبان متن نوشتاري يا گفتاري و مانند آن

انگلیسی

عنوان اصلي

Strictly convex submanifolds and hypersurfaces of positive curvature

نام عام مواد

[Thesis]

نام نخستين پديدآور

M. Ghomi

نام ساير پديدآوران

J. Spruck

نام ناشر، پخش کننده و غيره

The Johns Hopkins University

تاریخ نشرو بخش و غیره

1998

نام خاص و کميت اثر

107

جزئيات پايان نامه و نوع درجه آن

Ph.D.

کسي که مدرک را اعطا کرده

The Johns Hopkins University

امتياز متن

1998

متن يادداشت

We characterize submanifolds of Euclidean space which lie on closed hypersurfaces of positive curvature, and develop some applications of this result for boundary value problems via Monge-Ampere equations, smoothing of convex polytopes, and an extension of Hadamard's ovaloid theorem to hypersurfaces with boundary. The main result of this dissertation states that every smooth compact submanifold M of Euclidean space lies embedded in a smooth closed hypersurface of positive curvature if, and only if, M is strictly convex, i.e., through every point of M there passes a hyperplane, with contact of order one, with respect to which M lies strictly on one side. As applications of this result we show: (1) Every smooth closed strictly convex submanifold of codimension two bounds a smooth hypersurface of constant positive curvature. (2) Let M be a closed strictly convex submanifold of codimension 2; then, if M is usdC\sp{3,1}usd, the two hypersurfaces making up the boundary of the convex hull of M are each usdC\sp{1,1}usd; this result is optimal. (3) Every polytope P may be approximated arbitrarily closely by a closed hypersurface of nonnegative curvature which coincides with the boundary of P everywhere outside any given open neighborhood of the singular points. (4) Let M be a compact connected hypersurface of positive curvature in Euclidean n-space, usdn \ge 3usd, then M is strictly convex, if, and only if, each boundary component of M lies strictly on one side of the tangent hyperplanes of M at that component. Furthermore, we discuss some applications for self-linking number of space curves, and umbilic points of ovaloids.

موضوع مستند نشده

Mathematics

موضوع مستند نشده

Pure sciences

مستند نام اشخاص تاييد نشده

J. Spruck

مستند نام اشخاص تاييد نشده

M. Ghomi

نام الکترونيکي

فرمت انتشار

p

نوع ماده

[Thesis]

کد کاربرگه

276903

سطح دسترسي

a

تكميل شده

Y