https://hdl.handle.net/10481/29855 Fri, 10 Apr 2026 15:51:07 GMT 2026-04-10T15:51:07Z https://hdl.handle.net/10481/112433 The Newton’s problem assuming non-constant density of the fluid López Camino, Rafael This paper investigates the Newton’s problem of minimal resistance for a body moving through a fluid whose density decreases exponentially with altitude. We prove the local existence and regularity of radial solutions u (r) satisfying the initial conditions u(0)=u(0)=0 using a fixed point theorem. We show that the maximal domain of the solution is finite, (0,rM), terminating at a critical slope u(rM)= 1V https://hdl.handle.net/10481/112433 https://hdl.handle.net/10481/112223 Every Nonflat Conformal Minimal Surface is Homotopic to a Proper One Vrhovnik, Tjaša Given an open Riemann surface M, we prove that every nonflat conformal minimal immersion M → R^n (n ≥ 3) is homotopic through nonflat conformalminimal immersions M → R^n to a proper one. If n ≥ 5, it may be chosen in addition injective, hence a proper conformal minimal embedding. Prescribing its flux, as a consequence, every nonflat conformal minimal immersion M → R^n is homotopic to the real part of a proper holomorphic null embedding M → C^n. We also obtain a result for a more general family of holomorphic immersions from an open Riemann surface into C^n directed by Oka cones in C^n. This research is partially supported by the State Research Agency (AEI) via the grant no. PID2023-150727NB-I00, funded by MICIU/AEI/10.13039/501100011033 and ERDF/EU, Spain. Funding for open access publishing: Universidad de Granada/CBUA. https://hdl.handle.net/10481/112223 https://hdl.handle.net/10481/110084 Two classification results for stationary surfaces of the least moment of inertia López Camino, Rafael A surface in Euclidean space R3 is said to be an α-stationary surface if it is a critical point of the energy ∫Σ|p|α, where α∈R. These surfaces are characterized by the Euler-Lagrange equation H(p)=α⟨N(p),p⟩|p|2, p∈Σ, where H and N are the mean curvature and the normal vector of Σ. If α≠0, we prove that vector planes are the only ruled α-stationary surfaces. The second result of classification asserts that if α≠−2,−4, any α-stationary surface foliated by circles must be a surface of revolution. If α=−4, the surface is the inversion of a plane, a helicoid, a catenoid or an Riemann minimal example. If α=−2, and besides spheres centered at 0, we find non-spherical cyclic −-stationary surfaces. The author has been partially supported by MINECO/MICINN/FEDER grant no. PID2023-150727NB-I00, and by the “María de Maeztu” Excellence Unit IMAG, reference CEX2020-001105- M, funded by MCINN/AEI/10.13039/ 501100011033/ CEX2020-001105-M. https://hdl.handle.net/10481/110084 https://hdl.handle.net/10481/110083 Stationary surfaces for the moment of inertia with constant Gauss curvature López Camino, Rafael Consider the energy Eα⁢[Σ]=∫Σ|p|α𝑑�Σ, where Σ is a surface in Euclidean space ℝ3 and α∈ℝ. We prove that planes and spheres are the only stationary surfaces for Eα with constant Gauss curvature. We also characterize these surfaces assuming that a principal curvature is constant or that the mean curvature is constant. The author has been partially supported by MINECO/MICINN/FEDER grant no. PID2023-150727NB-I00, and by the “María de Maeztu” Excellence Unit IMAG, reference CEX2020-001105- M, funded by MCINN/AEI/10.13039/ 501100011033/CEX2020-001105-M. https://hdl.handle.net/10481/110083 https://hdl.handle.net/10481/110081 Singular minimal surfaces with constant curvature López Camino, Rafael We prove that singular minimal surfaces with constant Gauss curvature are planes, spheres, and cylindrical surfaces. We also classify all singular minimal surfaces with a constant principal curvature and singular minimal surfaces with constant mean curvature. The author has been partially supported by MINECO/MICINN/FEDER grant no. PID2023-150727NB-I00, and by the “María de Maeztu” Excellence Unit IMAG, reference CEX2020-001105-M, funded by MCINN/AEI/10.13039/501100011033/CEX2020-001105-M. https://hdl.handle.net/10481/110081