Cross-2D-to-3D (2D-3D) heterogeneous palmprint recognition aims to matching a 2D palmprint probe with the 3D palmprint galleries, which shows great potential for biometric applications due to rich information of 3D images and the low-cost of 2D image acquisition. However, the large structural discrepancy between 2D and 3D palmprint images makes it hard to directly conduct matching between 2D-3D heterogeneous palmprint images. In this paper, we propose a palmprint image generative adversarial network (PIGAN) to convert 2D palmprint images into 3D domain for 2D-3D heterogeneous palmprint recognition. We first calculate the mean curvature images (MCIs) to present the 3D palm surface measurements of 3D palmprint images. Then, we employ an image-to-image generation backbone to transform 2D palmprint images into 3D MCI representations. To make the fake MCIs realistic, we impose both adversarial and identity-aware learning losses to protect the discriminative information of MCIs, and further introduce a visual-recovery loss to restore the visual-specific texture characteristics of palmprints. By this way, high-quality 3D palmprint MCI can be synthesized with high similarity as the real ones at both feature and visual levels, such that the pixel-level gap between 2D and 3D palmprint images can be effectively reduced for 2D-3D heterogeneous palmprint recognition. Extensive experimental results on the widely-used PolyU 2D-3D palmprint database clearly show the effectiveness of the proposed PIGAN in improving the performance of 2D-3D heterogeneous palmprint recognition.