Research Papers and Preprints

1. Embedded minimal surfaces in S^3 and B^3 via equivariant eigenvalue optimization
   (with Mikhail Karpukhin, Robert Kusner, Daniel Stern).
   
2. On the areas of genus zero free minimal surfaces embedded in the unit 3-ball
   (with Jiahua Zou).
   
3. Free boundary minimal annuli immersed in the unit 3-ball
   (with Nikolaos Kapouleas).
   
4. Generalizing the linearized doubling approach and new minimal surfaces
   and self-shrinkers via doubling (with Nikolaos Kapouleas).
   Camb. J. Math. 11 (2023) no. 2 299-439
   
5. On the Canham problem: bending energy minimizers for any genus and
   isoperimetric ratio (with Robert Kusner). Arch. Ration. Mech. Anal. 247 (2023)
   
6. On Steklov eigenspaces for free boundary minimal surfaces in the unit ball
   (with Robert Kusner). To appear, Amer. J. Math.
   
7. Symmetry and isoperimetry for Riemannian surfaces (with Joe Hoisington).
   Calc. Var. Partial Differential Equations 61 (2022) no. 1
   
8. An isoperimetric deficit formula J. Geom. Anal. 31 (2021), no. 4, 3273–3279.
9. Minimal surfaces in the round three-sphere by doubling the equatorial two-sphere, II
   (with Nikolaos Kapouleas). Comm. Pure Appl. Math. 72 (2019), 2121-2195 
10. Area bounds for free boundary minimal surfaces in a geodesic ball in the sphere
    (with Brian Freidin). J. Funct. Anal. 277 No. 11 (2019), 108276.
11. Sharp area bounds for free boundary minimal surfaces in conformally euclidean balls
    (with Brian Freidin). Int. Math. Res. Not. IMRN 2020, no. 18, 5630–5641.
12. Rotational symmetry of asymptotically conical mean curvature flow self-expanders
    (with Frederick Tsz-Ho Fong). Comm. Anal. Geom. 27 No. 3 (2019), 599-618
13. A characterization of the critical catenoid
    Indiana University Mathematics Journal, 67, No. 2 (2018), 889-897.
14. Free boundary minimal surfaces in the unit ball with low cohomogeneity
    (with Brian Freidin, Mamikon Gulian).Proc. Amer. Math. Soc. 145 (2017), no. 4, 1671-1683.

Research with Undergraduates

1. On Liouville's theorem for conformal maps
   (with Mathew Kushelman).
To appear, The American Mathematical Monthy
2. Two-point functions and constant mean curvature surfaces in euclidean three-space
   (with Everett Meekins). Involve 16 (2023) no. 3, 467-482.

Other Publications

1. Bases for second order linear ODEs
   The American Mathematical Monthy Vol. 127, No. 9 (2020), pp. 849. 
2. Newton's shell theorem via Archimedes's hat box and single-variable calculus
   College Math. J. 49 (2018), no. 2, 109–113.  2019 George Polya Award Winner
3. A note regarding Hopf's umlaufsatz
   The American Mathematical Monthly Vol. 125, No. 6 (June 2018), pp. 541-544.
4. On the smooth Jordan Brouwer separation theorem
   The American Mathematical Monthly Vol. 123, No. 3 (March 2016), pp. 292-295.
5. An extremely short proof of the hairy ball theorem
   The American Mathematical Monthly Vol. 123, No. 5 (May 2016), pp. 502-503.
6. Another proof of Clairaut's theorem
   The American Mathematical Monthly Vol. 121, No. 2 (February 2014), pp. 165-166.
7. The Poincare-Hopf index theorem and the fundamental theorem of algebra*
   The Princeton Undergraduate Mathematics Journal Summer 2016, pp. 34-38.
8. Trigonometric derivatives made easy*
   The College Mathematics Journal, vol. 47, no. 5 (November 2016), pp. 365–366
9. On the derivatives of the trigonometric functions the easy way (Hebrew translation)*
   Ale”h - Bulletin for the Mathematics Teacher (Israel), Issue 55, pp. 60-61. [In Hebrew]
10. An alternative approach to the product rule*
    The American Mathematical Monthly Vol. 123, No. 5 (May 2016), p. 470.
11. Problem 361 (with Brian Freidin)
    Math Horizons Vol. 25, Issue 1 (September 2017), pp. 28.
12. Problem 11953
    The American Mathematical Monthly Vol. 118, No. 8 (October 2011), pp. 747-754.
13. Problem 1889 (with Gary Gordon)
    Mathematics Magazine Vol. 85, No. 1 (February 2012), pp. 61-68.

*Written under the pseudonym Piotr Josevich.