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Polynomial Solutions to the Minimal ...

Guo, Yifan,

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Polynomial Solutions to the Minimal Surface Equation and Green Functions on Singular Minimal Submanifolds /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Polynomial Solutions to the Minimal Surface Equation and Green Functions on Singular Minimal Submanifolds // Yifan Guo.
作者:	Guo, Yifan,
面頁冊數:	1 electronic resource (122 pages)
附註:	Source: Dissertations Abstracts International, Volume: 87-01, Section: B.
Contained By:	Dissertations Abstracts International87-01B.
標題:	Mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32113073
ISBN:	9798288800948

Polynomial Solutions to the Minimal Surface Equation and Green Functions on Singular Minimal Submanifolds /
Guo, Yifan,

Polynomial Solutions to the Minimal Surface Equation and Green Functions on Singular Minimal Submanifolds /Yifan Guo. - 1 electronic resource (122 pages)

Source: Dissertations Abstracts International, Volume: 87-01, Section: B.

One of the classical problems in the calculus of variations is the Plateau problem, which seeks an area-minimizing hypersurface spanning a prescribed boundary. This thesis is devoted to the study of two problems closely connected to area-minimizing hypersurfaces.The first problem investigates nonlinear polynomials that solve the minimal surface equation. By applying the area-minimizing property to the study of polynomial solutions - a perspective not previously developed in the literature - we investigate the constraints that such solutions must satisfy. We prove a structure theorem on polynomial solutions and use it to show that the structure of a polynomial solution is highly restricted.The second problem concerns the construction of Green functions on singular minimal sub-manifolds, with a focus on area-minimizing boundaries. We construct the Green function on a stationary integral varifold with Euclidean volume growth and establish convergence of Green functions under convergence of area-minimizing boundaries. We use it to analyze the asymptotic behavior of the Green function near the pole and at infinity and deduce a universal upper and lower bound.

English

ISBN: 9798288800948Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Green functions

Polynomial Solutions to the Minimal Surface Equation and Green Functions on Singular Minimal Submanifolds /
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245 1 0 $a Polynomial Solutions to the Minimal Surface Equation and Green Functions on Singular Minimal Submanifolds / $c Yifan Guo.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2025
300 $a 1 electronic resource (122 pages)
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337 $a computer $b c $2 rdamedia
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500 $a Source: Dissertations Abstracts International, Volume: 87-01, Section: B.
500 $a Advisors: Schoen, Richard Committee members: Streets, Jeffrey; Mooney, Connor.
502 $b Ph.D. $c University of California, Irvine $d 2025.
520 $a One of the classical problems in the calculus of variations is the Plateau problem, which seeks an area-minimizing hypersurface spanning a prescribed boundary. This thesis is devoted to the study of two problems closely connected to area-minimizing hypersurfaces.The first problem investigates nonlinear polynomials that solve the minimal surface equation. By applying the area-minimizing property to the study of polynomial solutions - a perspective not previously developed in the literature - we investigate the constraints that such solutions must satisfy. We prove a structure theorem on polynomial solutions and use it to show that the structure of a polynomial solution is highly restricted.The second problem concerns the construction of Green functions on singular minimal sub-manifolds, with a focus on area-minimizing boundaries. We construct the Green function on a stationary integral varifold with Euclidean volume growth and establish convergence of Green functions under convergence of area-minimizing boundaries. We use it to analyze the asymptotic behavior of the Green function near the pole and at infinity and deduce a universal upper and lower bound.
546 $a English
590 $a School code: 0030
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Applied mathematics. $3 2122814
650 4 $a Theoretical physics. $3 2144760
653 $a Green functions
653 $a Minimal surface equation
653 $a Polynomial solution
653 $a Singular minimal submanifolds
653 $a Plateau problem
690 $a 0405
690 $a 0642
690 $a 0753
690 $a 0364
710 2 $a University of California, Irvine. $b Mathematics. $e degree granting institution. $3 3823182
720 1 $a Schoen, Richard $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 87-01B.
790 $a 0030
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32113073