Publikationen Ulrich Dierkes

Preprints

Dierkes, U.; Groh, N. : Symmetric Solutions of the Singular Minimal Surface Equation. To appear

Refereed publications

Dierkes, Ulrich: Removable Singularities of Solutions of the Symmetric Minimal Surface Equation.
Vietnam Journal of Mathematics, (2020), in press abstract

Dierkes, Ulrich: On solutions of the singular minimal surface equation. Ann. Mat. Pura Appl. (4) 198 (2019), no. 2, 505–516. abstract
 
Dierkes, Ulrich; Jenschke, Tristan; Pozzi, Paola: Approximation of minimal surfaces with free boundaries. Interfaces Free Bound. 20 (2018), no. 4, 551–576. abstract
 

Dierkes, Ulrich; Tennstädt, Tobias: Bernstein results for symmetric minimal surfaces of controlled growth. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 18 (2018), no. 4, 1285–1309. abstract
 

Dierkes, Ulrich; Schwab, Dirk: Maximum principles for submanifolds of arbitrary codimension and bounded mean curvature. Calc. Var. Partial Differential Equations 22 (2005), no. 2, 173–184. abstract
 

Dierkes, Ulrich: On the regularity of solutions for a singular variational problem. Math. Z. 225 (1997), no. 4, 657–670. pdf
 
Dierkes, Ulrich; Huisken, Gerhard: The N-dimensional analogue of the catenary: prescribed area. Geometric analysis and the calculus of variations, 1–12, Int. Press, Cambridge, MA, 1996. abstract
 
Dierkes, Ulrich: Curvature estimates for minimal hypersurfaces in singular spaces. Invent. Math. 122 (1995), no. 3, 453–473. abstract
 
Dierkes, U.: A Bernstein result for energy minimizing hypersurfaces. Calc. Var. Partial Differential Equations 1 (1993), no. 1, 37–54. abstract
 

Dierkes, Ulrich: A Hamilton Jacobi theory for singular Riemannian metrics. Arch. Math. (Basel) 61 (1993), no. 3, 260–271. pdf
 
Dierkes, Ulrich: Über singuläre Lösungen gewisser mehrdimensionaler Variationsprobleme. (German) [On singular solutions of certain multidimensional variational problems] Ann. Univ. Sarav. Ser. Math. 3 (1990), no. 2, 38–107.
 
Dierkes, Ulrich: On the nonexistence of energy stable minimal cones. Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990), no. 6, 589–601. abstract
 
Dierkes, Ulrich: Maximum principles and nonexistence results for minimal submanifolds. Manuscripta Math. 69 (1990), no. 2, 203–218. abstract
 
Dierkes, U.; Huisken, G.: The n-dimensional analogue of the catenary: existence and nonexistence. Pacific J. Math. 141 (1990), no. 1, 47–54. pdf
 
Dierkes, U.: A geometric maximum principle for surfaces of prescribed mean curvature in Riemannian manifolds. Z. Anal. Anwendungen 8 (1989), no. 2, 97–102. abstract
 
Dierkes, Ulrich: A classification of minimal cones in Rn×R+ and a counterexample to interior regularity of energy minimizing functions. Manuscripta Math. 63 (1989), no. 2, 173–192. abstract
 
Dierkes, Ulrich: Boundary regularity for solutions of a singular variational problem with linear growth. Arch. Rational Mech. Anal. 105 (1989), no. 4, 285–298. abstract
 
Dierkes, Ulrich: Minimal hypercones and C0,1/2 minimizers for a singular variational problem. Indiana Univ. Math. J. 37 (1988), no. 4, 841–863. abstract
   
Dierkes, Ulrich: A geometric maximum principle, Plateau's problem for surfaces of prescribed mean curvature, and the two-dimensional analogue of the catenary. Partial differential equations and calculus of variations, 116–141, Lecture Notes in Math., 1357, Springer, Berlin, 1988. abstract
   
Bemelmans, J., Dierkes, U. : On a singular variational integral with linear growth. I. Existence and regularity of minimizers. Arch. Rational Mech. Anal. 100 (1987), no. 1, 83–103. abstract
   
Dierkes, U.; Hildebrandt, S.; Lewy, H.: On the analyticity of minimal surfaces at movable boundaries of prescribed length. J. Reine Angew. Math. 379 (1987), 100–114. abstract
   
Dierkes, Ulrich: Plateau's problem for surfaces of prescribed mean curvature in given regions. Manuscripta Math. 56 (1986), no. 3, 313–331. abstract

Monographs

Dierkes, Ulrich; Hildebrandt, Stefan; Tromba, Anthony J.: Global analysis of minimal surfaces. Revised and enlarged second edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 341. Springer, Heidelberg, 2010. xvi+537 pp. ISBN: 978-3-642-11705-3. abstract

Dierkes, Ulrich; Hildebrandt, Stefan; Tromba, Anthony J.: Regularity of minimal surfaces. Revised and enlarged second edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 340. Springer, Heidelberg, 2010. xviii+623 pp. ISBN: 978-3-642-11699-5. abstract

Dierkes, Ulrich; Hildebrandt, Stefan; Sauvigny, Friedrich: Minimal surfaces. Revised and enlarged second edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 339. Springer, Heidelberg, 2010. xvi+688 pp. ISBN: 978-3-642-11697-1. abstract

Dierkes, Ulrich; Hildebrandt, Stefan; Küster, Albrecht; Wohlrab, Ortwin: Minimal surfaces. II. Boundary regularity. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 296. Springer-Verlag, Berlin, 1992. xii+422 pp. ISBN: 3-540-53170-X. abstract
 
Dierkes, Ulrich; Hildebrandt, Stefan; Küster, Albrecht; Wohlrab, Ortwin: Minimal surfaces. I. Boundary value problems. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 295. Springer-Verlag, Berlin, 1992. xiv+508 pp. ISBN: 3-540-53169-6. abstract

Further publications, contributions to proceedings etc.

Dierkes, Ulrich: Singular minimal surfaces. Geometric analysis and nonlinear partial differential equations, 177–193, Springer, Berlin, 2003. abstract
 
Dierkes, Ulrich: Minimal surfaces in singular spaces. European Congress of Mathematics, Vol. I (Budapest, 1996), 150–161, Progr. Math., 168, Birkhäuser, Basel, 1998.
 
Dierkes, Ulrich: On singular variational problems. Workshop on Theoretical and Numerical Aspects of Geometric Variational Problems (Canberra, 1990), 89–106, Proc. Centre Math. Appl. Austral. Nat. Univ., 26, Austral. Nat. Univ., Canberra, 1991. pdf
 
Dierkes, Ulrich: Singuläre Variationsprobleme und Hindernisprobleme. (German) [Singular variational problems and obstacle problems] Dissertation, Rheinische Friedrich-Wilhelms-Universität, Bonn, 1984. Bonner Mathematische Schriften [Bonn Mathematical Publications], 155. Universität Bonn, Mathematisches Institut, Bonn, 1984. i+90 pp.
 
Dierkes, Ulrich: Isoperimetrische Variationsprobleme. (German) [Isoperimetric variational problems] Diplomarbeit, Universität Bonn, Bonn, 1979. Bonner Mathematische Schriften [Bonn Mathematical Publications], 132. Universität Bonn, Mathematisches Institut, Bonn, 1981. ii+49 pp