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Some Geometric Inequalities by the ABP Method.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Some Geometric Inequalities by the ABP Method./
Author:	Pham, The Doanh.
Description:	1 online resource (68 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 84-12, Section: B.
Contained By:	Dissertations Abstracts International84-12B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30317310click for full text (PQDT)
ISBN:	9798379592561

Some Geometric Inequalities by the ABP Method.
Pham, The Doanh.

Some Geometric Inequalities by the ABP Method. - 1 online resource (68 pages)

Source: Dissertations Abstracts International, Volume: 84-12, Section: B.

Thesis (Ph.D.)--Rutgers The State University of New Jersey, School of Graduate Studies, 2023.

Includes bibliographical references

In this thesis, we apply the so-called Alexandrov-Bakelman-Pucci (ABP) method to establish some geometric inequalities. We first prove a logarithmic Sobolev inequality for closed n-dimensional minimal submanifolds Σ of \uD835\uDD4An+m. As a consequence, it recovers the classical result that |\uD835\uDD4An| ≤ |Σ| for m = 1, 2. Next, we prove a Sobolev type inequality for positive symmetric two-tensors on smooth domains in ℝn which was established by D. Serre when the domain is convex. Furthermore, we formulate and prove an inequality related to quermassintegrals of closed hypersurfaces of the Euclidean space. In the last application of the ABP method, we give a proof of the Willmore-type inequality for k-curvatures of closed submanifolds in a manifold with nonnegative sectional curvature.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798379592561Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Alexandrov-Bakelman-PucciIndex Terms--Genre/Form:

542853
Electronic books.

Some Geometric Inequalities by the ABP Method.
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245 1 0 $a Some Geometric Inequalities by the ABP Method.
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500 $a Source: Dissertations Abstracts International, Volume: 84-12, Section: B.
500 $a Advisor: Li, YanYan.
502 $a Thesis (Ph.D.)--Rutgers The State University of New Jersey, School of Graduate Studies, 2023.
504 $a Includes bibliographical references
520 $a In this thesis, we apply the so-called Alexandrov-Bakelman-Pucci (ABP) method to establish some geometric inequalities. We first prove a logarithmic Sobolev inequality for closed n-dimensional minimal submanifolds Σ of \uD835\uDD4An+m. As a consequence, it recovers the classical result that |\uD835\uDD4An| ≤ |Σ| for m = 1, 2. Next, we prove a Sobolev type inequality for positive symmetric two-tensors on smooth domains in ℝn which was established by D. Serre when the domain is convex. Furthermore, we formulate and prove an inequality related to quermassintegrals of closed hypersurfaces of the Euclidean space. In the last application of the ABP method, we give a proof of the Willmore-type inequality for k-curvatures of closed submanifolds in a manifold with nonnegative sectional curvature.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Alexandrov-Bakelman-Pucci
653 $a Geometric inequalities
653 $a Sobolev inequality
655 7 $a Electronic books. $2 lcsh $3 542853
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710 2 $a ProQuest Information and Learning Co. $3 783688
710 2 $a Rutgers The State University of New Jersey, School of Graduate Studies. $b Mathematics. $3 3698280
773 0 $t Dissertations Abstracts International $g 84-12B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30317310 $z click for full text (PQDT)