Papers by Harold R. Parks

The Lagrange inversion theorem in the smooth case (with Steven G. Krantz)
Journal of Mathematical Analysis and Applications
volume 340, number 2
April 2007
pages 1263-1270

A slope-bounding procedure for mass-minimizing currents
International Journal of Applied Mathematics & Statistics
volume 10, number S07
September 2007
pages 25-37

The generalization of Faulhaber's formula to sums of non-integral powers
(with Kevin J. McGown)
Journal of Mathematical Analysis and Applications
volume 330, number 1
June 2007
pages 571-575

Symmetrized-lexicographic order and the method of points
Journal of Mathematical Analysis and Applications
volume 324, number 2
December 2006
pages 934-940

Geometric characterizations of centroids of simplices
(with Steven G. Krantz and John E. McCarthy)
Journal of Mathematical Analysis and Applications
volume 316, number 1
April 2006
pages 87-109

Review of Strange Curves, Counting Rabbits, and Other Mathematical Explorations by Keith Ball,
Notices of the American Mathematical Society
volume 51, number 11
December 2004
pages 1352-1354

Sums of non-integral powers
Journal of Mathematical Analysis and Applications
volume 297, number 1
September 2004
pages 343-349

An elementary calculation of the dihedral angle of the regular n-simplex
(with Dean C. Wills)
American Mathematical Monthly
volume 109, number 8
October 2002
pages 756-758

Energy estimates for area minimizing
hypersurfaces with arbitrary boundaries
(with Jon T. Pitts)
Journal of Computational and Applied Mathematics
volume 115, numbers 1 and 2
March 2000,
pages 451-460

Surfaces minimizing integrals of divergent integrands
in "Analysis of Divergence: control and management of divergent processes"
edited by William O. Bray and Caslav V. Stanojevic
Birkhauser, 1999
pages 441-462

Minimal surfaces with constant contact angle
(with Kirk Lancaster)
in "Nonlinear Mathematical Analysis and its Applications"
edited by T. M. Rassias
Hadronic Press, 1998
pages 109-126

Computing least area hypersurfaces spanning arbitrary boundaries
(with Jon T. Pitts)
SIAM Journal on Scientific Computing
volume 18, number 3
May 1997
pages 886-917

The least gradient method for computing area minimizing
hypersurfaces spanning arbitrary boundaries
(with Jon T. Pitts)
Journal of Computational and Applied Mathematics
volume 66, numbers 1 and 2
January 1996
pages 401-409

The least gradient method for computing area-minimizing hypersurfaces
in "Statistical Thermodynamics and Differential
Geometry of Microstructured Material"
edited by H. T. Davis and J. C. C. Nitsche
The IMA Volumes in Mathematics and Its Applications, 51
Springer-Verlag, 1993
pages 99-116

A Jordan arc in R^m with positive m-dimensional Lebesgue measure
(with Richard M. Schori)
in "The Problem of Plateau - A Tribute to Jesse Douglas and Tibor Rado"
edited by T. M. Rassias
World Scientific Publishing, River Edge, NJ, 1992
pages 229-236

Soap-film-like minimal surfaces spanning knots
Journal of Geometric Analysis
volume 2 (1992), number 3
pages 267-290

Numerical approximation of parametric oriented area-minimizing hypersurfaces
SIAM Journal on Scientific and Statistical Computing
volume 13 (1992), number 2
pages 499-511

On the vector sum of two convex sets in space
(with Steven G. Krantz)
Canadian Journal of Mathematicsa
volume 43 (1991), number 2
pages 347-355

Numerical approximation of area-minimizing hypersurfaces
in "Computing Optimal Geometries"
edited by J. E. Taylor
American Mathematical Society
videotape and accompanying abstracts, 1991

An application of the Cauchy-Kowalewsky Theorem:
The minimal surface equation at corners
in "Topics in Mathematical Analysis"
edited by T. M. Rassias
Series in Pure Mathematics, 11, World Scientific Publishing, Teaneck, NJ, 1989
pages 741-757

Partial regularity of functions of least gradient in R⁸
Annali della Scuola Normale Superiore di Pisa
Classe di Scienze, Serie IV
volume 15 (1988), number 3
pages 447-451

Existence and Lipschitz regularity of functions minimizing integrals of
certain positively homogeneous integrands
Communications in Partial Differential Equations
volume 13, number 8
August 1988
pages 927-983

A strong approximation theorem for real cycles
Indiana University Mathematics Journal
volume 35, number 3
Fall 1986
pages 449-450

Explicit Determination of Area Minimizing Hypersurfaces, II
Memoirs of the American Mathematical Society, No. 342 (1986), iv + 90 pages
(This item has the ISBN 0821823396, so it also may be treated as a book)

Nonlinear conditions for differentiability of functions
(with John Duncan and Steven G. Krantz)
Journal d'Analyse Mathematique
volume 45 (1985)
pages 46-68

The coincidence set for two-dimensional area minimizing surfaces in Rⁿ
which avoid a convex obstacle
in "Differential Geometry, Calculus of Variations, and Their Applications"
edited by G. M. Rassias and T. M. Rassias
Lecture Notes in Pure and Applied Mathematics, 100,
Marcel Dekker, 1985
pages 385-389

Jacobi fields and regularity of functions of least gradient
(with William P. Ziemer)
Annali della Scuola Normale Superiore di Pisa
Classe di Scienze, Serie IV
volume 11 (1984), number 4
pages 505-527

Regularity of solutions to elliptic isoperimetric problems
Pacific Journal of Mathematics
volume 113, number 2
August 1984
pages 463-470

Elliptic isoperimetric problems
Indiana University Mathematics Journal
volume 30, number 6
November-December 1981
pages 937-958

Distance to C^k hypersurfaces
(with Steven G. Krantz)
Journal of Differential Equations
volume 40, number 1
April 1981
pages 116-120

The Gauss map of a three-dimensional minimal surface
Journal of Differential Geometry
volume 16, number 1
March 1981
pages 75-81

Some new constructions and estimates in the problem of least area
Transactions of the American Mathematical Society
volume 248, number 2
March 1979
pages 311-346

Explicit determination of area minimizing hypersurfaces
Duke Mathematical Journal
volume 44, number 3
September 1977
pages 519-534

A method for computing non-parametric area minimizing hypersurfaces
over n dimensional domains, together with a priori error estimates
Indiana University Mathematics Journal
volume 26, number 4
July-August 1977
pages 625-643