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Mathematics

[6261] Solution of the Plateau problem for$m$-dimensional surfaces of varying topological type

E. R. Reifenberg Bristol

TBD mathscidoc:1701.331198

Acta Mathematica, 104, (1), 1-92, 1959.4

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Kenig C E, Toro T. Poisson kernel characterization of Reifenberg flat chord arc domains[J]. Annales Scientifiques De L Ecole Normale Superieure, 2003, 36(3): 323-401.

Blank I. Sharp results for the regularity and stability of the free boundary in the obstacle problem[J]. Indiana University Mathematics Journal, 2001, 50(3): 1077-1112.

Strzelecki P, Der Mosel H V. Integral Menger curvature for surfaces[J]. Advances in Mathematics, 2009, 226(3): 2233-2304.

Azzam J, Schul R. Hard Sard: Quantitative Implicit Function and Extension Theorems for Lipschitz Maps[J]. Geometric and Functional Analysis, 2011, 22(5): 1062-1123.

Byun S, Ok J, Ryu S, et al. Global gradient estimates for general nonlinear parabolic equations in nonsmooth domains[J]. Journal of Differential Equations, 2013, 254(11): 4290-4326.

David G. $C^{1+\\alpha}$-Regularity for Two-Dimensional Almost-Minimal Sets in $\\R^n$[J]. Journal of Geometric Analysis, 2008, 20(4): 837-954.

Kleiner B, Lott J. Locally Collapsed 3-Manifolds[C]., 2010.

Byun S, Palagachev D K. Morrey regularity of solutions to quasilinear elliptic equations over Reifenberg flat domains[J]. Calculus of Variations and Partial Differential Equations, 2012: 37-76.

Lemenant A, Milakis E, Spinolo L V, et al. On the extension property of Reifenberg-flat domains[J]. Annales Academiae Scientiarum Fennicae. Mathematica, 2012: 51-71.

Tobias H Colding. New monotonicity formulas for Ricci curvature and applications. I. 2012.

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[6262] Non-parametric surfaces given by linearly continuous functions

Casper Goffman Pardue University, Lafayette, Ind., U.S.A.

TBD mathscidoc:1701.331197

Acta Mathematica, 103, (3), 269-291, 1959.7

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Botsko M W, Gosser R A. On the Differentiability of Functions of Several Variables[J]. American Mathematical Monthly, 1985, 92(9).

Brandi P, Salvadori A. On convergence in area in the generalized sense[J]. Journal of Mathematical Analysis and Applications, 1983, 92(1): 119-138.

Fesq R M. Green’s formula, linear continuity, and Hausdorff measure[J]. Transactions of the American Mathematical Society, 1965: 105-112.

Goffman C. A characterization of linearly continuous functions whose partial derivatives are measures[J]. Acta Mathematica, 1967, 117(1): 165-190.

Berger M S, Meyers N G. On a system of nonlinear partial differential equations arising in mathematical economics[J]. Bulletin of the American Mathematical Society, 1966, 72(6): 954-958.

William P Ziemer. The area and variation of linearly continuous functions. 1969.

Goffman C. Coordinate invariance of linear continuity[J]. Archive for Rational Mechanics and Analysis, 1965, 20(2).

Goffman C. Decomposition of functions whose partial derivatives are measures[J]. Mathematika, 1968, 15(02): 149-152.

Casper Goffman. Area of discontinuous surfaces. 1961.

Casper Goffman. Linearly continuous functions of finite area. 1966.

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[6263] Polyhedral sections of convex bodies

Victor Klee Copenhagen

TBD mathscidoc:1701.331196

Acta Mathematica, 103, (3), 243-267, 1959.9

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David W Walkup · Roger J B Wets. Continuity of some convex-cone-valued mappings. 1967.

Schffer J J. Inner diameter, perimeter, and girth of spheres[J]. Mathematische Annalen, 1967, 173(1): 59-82.

Walkup D W, Wets R J. A LIPSCHITZIAN CHARACTERIZATION OF CONVEX POLYHEDRA[J]. Proceedings of the American Mathematical Society, 1969, 23(1): 167-173.

Robert Deville · V P Fonf · Petr Hajek. Analytic and polyhedral approximation of convex bodies in separable polyhedral Banach spaces. 1998.

Lazar A J. Spaces of affine continuous functions on simplexes[J]. Transactions of the American Mathematical Society, 1968, 134(3): 503-525.

Fonf V P. Polyhedral Banach spaces[J]. Mathematical Notes, 1981, 30(4): 809-813.

Fonf V P. Three characterizations of polyhedral Banach spaces[J]. Ukrainian Mathematical Journal, 1990, 42(9): 1145-1148.

Lindenstrauss J. Notes on Klee’s paper “Polyhedral sections of convex bodies”[J]. Israel Journal of Mathematics, 1966, 4(4): 235-242.

Fonf V P, Lindenstrauss J. Some results on infinite-dimensional convexity[J]. Israel Journal of Mathematics, 1998, 108(1): 13-32.

Aldo J Lazar. Polyhedral banach spaces and extensions of compact operators. 1969.

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[6264] Maximal algebras of continuous functions

K. Hoffman Massachusetts Institute of Technology, Massachusets, USA I. M. Singer Massachusetts Institute of Technology, Massachusets, USA

TBD mathscidoc:1701.331195

Acta Mathematica, 103, (3), 217-241, 1959.7

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Glicksberg I. Measures orthogonal to algebras and sets of antisymmetry[J]. Transactions of the American Mathematical Society, 1962, 105(3): 415-435.

Sarason D. Algebras of functions on the unit circle[J]. Bulletin of the American Mathematical Society, 1973, 79(2): 286-299.

Stolzenberg G. Polynomially and rationally convex sets[J]. Acta Mathematica, 1963, 109(1): 259-289.

John Wermer. Banach algebras and analytic functions. 1961.

E M Cirka. APPROXIMATION BY HOLOMORPHIC FUNCTIONS ON SMOOTH MANIFOLDS IN Cn. 1969.

Sidney S J. Properties of the sequence of closed powers of a maximal ideal in a sup-norm algebra[J]. Transactions of the American Mathematical Society, 1968, 131(1): 128-148.

Sun Yung A Chang. Structure of subalgebras between ^{∞} and ^{∞}. 1977.

Bishop C J. Approximating continuous functions by holomorphic and harmonic functions[J]. Transactions of the American Mathematical Society, 1989, 311(2): 781-811.

Shaujin Chang · D E Marshall. Some algebras of bounded analytic functions containing the disk algebra. 1977.

Norman L Alling. Extensions of meromorphic function rings over non-compact Riemann surfaces. II. 1966.

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[6265] On the theory of potentials in locally compact spaces

Bent Fuglede Copenhagen

TBD mathscidoc:1701.331194

Acta Mathematica, 103, (3), 139-215, 1959.6

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Amabili M, Pellicano F, Paidoussis M P, et al. NON-LINEAR DYNAMICS AND STABILITY OF CIRCULAR CYLINDRICAL SHELLS CONTAINING FLOWING FLUID. PART I: STABILITY[J]. Journal of Sound and Vibration, 1999, 225(4): 655-699.

Zorii N. Equilibrium Potentials with External Fields[J]. Ukrainian Mathematical Journal, 2003, 55(9): 1423-1444.

E Bendito · A Carmona · A M Encinas · J M Gesto. Estimation of Fekete points. 2007.

Hans Wallin. Continuous functions and potential theory. 1963.

Sikic H, Song R, Vondracek Z, et al. Potential Theory of Geometric Stable Processes[J]. Probability Theory and Related Fields, 2005, 135(4): 547-575.

Song R, Vondracek Z. Potential theory of subordinate killed Brownian motion in a domain[J]. Probability Theory and Related Fields, 2003, 125(4): 578-592.

Zorii N. Equilibrium Problems for Potentials with External Fields[J]. Ukrainian Mathematical Journal, 2003, 55(10): 1588-1618.

Ponnusamy S, Sahoo P K. Geometric properties of certain linear integral transforms[J]. Bulletin of The Belgian Mathematical Society-simon Stevin, 2005, 12(1): 95-108.

Zahle M. Riesz Potentials and Liouville Operators on Fractals[J]. Potential Analysis, 2004, 21(2): 193-208.

Lai H C, Wu S Y. Extremal points and optimal solutions for general capacity problems[J]. Mathematical Programming, 1992, 54(1): 87-113.

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Mathematics

[6261] Solution of the Plateau problem for$m$-dimensional surfaces of varying topological type

E. R. Reifenberg Bristol

TBD mathscidoc:1701.331198

[6262] Non-parametric surfaces given by linearly continuous functions

Casper Goffman Pardue University, Lafayette, Ind., U.S.A.

TBD mathscidoc:1701.331197

[6263] Polyhedral sections of convex bodies

Victor Klee Copenhagen

TBD mathscidoc:1701.331196

[6264] Maximal algebras of continuous functions

K. Hoffman Massachusetts Institute of Technology, Massachusets, USA I. M. Singer Massachusetts Institute of Technology, Massachusets, USA

TBD mathscidoc:1701.331195

[6265] On the theory of potentials in locally compact spaces

Bent Fuglede Copenhagen

TBD mathscidoc:1701.331194

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