Is there a cure for pulmonary hypertension?

Hard to tell. It depends on what the cause of it is. Obstructive sleep apnea if causing it, may be cured by weight loss and some surgical techniques, whereas primary pulmonary hypertension will not get cured but may be adequately controlled by some medications.
PH Cure. There are 9 available medications for pulmonary arterial hypertension (pah). The treatment can be quite effective but does not generally cure pah. Lung transplant can cure the disease but has other significant issues.
Depends. Depends on the cause. Most ph is due to lung disease. If the lung disease can be treated successfully, the ph resolves. Primary pulmonary hypertension is more difficult because there is no known cause but there are new medicines that are being used for pph with some success.